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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises find the derivative of the function.ƒ(x) = x² + 5 - 3x-2
In Exercises find an equation of the line that is tangent to the graph of and parallel to the given line. Function f(x) = x³ Line 3x = y + 1 = 0
In Exercises find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function y = 2x4 2x4 - 3 Point (1, -1)
In Exercises find an equation of the line that is tangent to the graph of and parallel to the given line. Function f(x) = x³ + 2 Line 3x - y - 4 = 0
In Exercises find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function y = (4x + 1)² Point (0, 1)
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results f(x) 6 x + 2³ (0, 3)
In Exercises find an equation of the line that is tangent to the graph of and parallel to the given line. Function f(x) = 2x² Line 4x + y + 3 = 0
In Exercises find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function ·ƒ(x) = − 1/2 + 3x³ Point (0, -¹)
In Exercises find an equation of the line that is tangent to the graph of and parallel to the given line. Function - f(x) = x² Line 2xy + 1 = 0
In Exercises find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function f(t) = 2 - 4 t Point (4,1)
In Exercises find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function f(x) 8 x² Point (2, 2)
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results f(x) = x + = ₂ X (-4,-5)
In Exercises complete the table to find the derivative of the function. Original Function 4 y = Rewrite Differentiate Simplify
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results f(x) = √√√x – 1, (5,2) -
In Exercises complete the table to find the derivative of the function. Original Function y X Rewrite Differentiate Simplify
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results (I 'I) *x^ = (x)ƒ
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph thefunction and its tangent line at the point(c) Use thederivative feature of a graphing utility to confirm your results f(x) = x² + 3, (-1,4)
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results f(x) = x³, (2,8)
In Exercises use the rules of differentiation to find the derivative of the function. 5 2 (2x)³ + 2 cos x
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point(c) Use the derivative feature of a graphing utility to confirm your results f(x) = x² + 2x-1, (1, 2)
In Exercises use the rules of differentiation to find the derivative of the function. y 1 X - 3 sin x
In Exercises complete the table to find the derivative of the function. Original Function Rewrite Differentiate 5 2x² y = Simplify
In exercises find the derivative of the function by the limit process. f(x) || 1 x2
In exercises find the derivative of the function by the limit process. f(x) = 4 √x
In exercises find the derivative of the function by the limit process. f(x) = √√x + 4
In Exercises use the rules of differentiation to find the derivative of the function. x 800²-2x = k
In exercises find the derivative of the function by the limit process. = 1 x 1
In Exercises use the rules of differentiation to find the derivative of the function.y = 7 + sin x
In Exercises use the rules of differentiation to find the derivative of the function.g(t) = π cos t
In exercises find the derivative of the function by the limit process.ƒ(x) = x3 + x2
In Exercises use the rules of differentiation to find the derivative of the function. y F|N TT 2 sin - cos 0
In exercises find the derivative of the function by the limit process.ƒ(x) = x³ - 12x
In Exercises use the rules of differentiation to find the derivative of the function.y = 2x³ + 6x² - 1
In exercises find the derivative of the function by the limit process.ƒ(x) = x2 - 5
In Exercises use the rules of differentiation to find the derivative of the function.s(t) = t³ + 5t² - 3t + 8
In exercises find the derivative of the function by the limit process.ƒ(x) = x² + x - 3
In exercises find the derivative of the function by the limit process. f(x) = 5 - 3x
In Exercises use the rules of differentiation to find the derivative of the function.y = 4x - 3x³
In exercises find the derivative of the function by the limit process. 2 h(s) = 3 + s
In Exercises use the rules of differentiation to find the derivative of the function.g(x) = x2 + 4x3
In Exercises use the rules of differentiation to find the derivative of the function.y = t² - 3t + 1
In exercises find the derivative of the function by the limit process.ƒ(x) = 7x - 3
In Exercises use the rules of differentiation to find the derivative of the function.ƒ(t) = -2t² + 3t - 6
In exercises find the derivative of the function by the limit process.ƒ(x) = -10x
In Exercises use the rules of differentiation to find the derivative of the function.g(x) = 6x + 3
In exercises find the derivative of the function by the limit process.g(x) = − 3
In Exercises use the rules of differentiation to find the derivative of the function.ƒ(x) = x + 11
In Exercises use the rules of differentiation to find the derivative of the function. x/7 = (x)8
In exercises find the derivative of the function by the limit process.ƒ(x) =7
In Exercises find the slope of the tangent line to the graph of the function at the given point. h(t) = t² + 4t, (1,5)
In Exercises use the rules of differentiation to find the derivative of the function. x/= (x)ƒ
In Exercises find the slope of the tangent line to the graph of the function at the given point. f(t) = 3t t², (0,0) -
In Exercises use the rules of differentiation to find the derivative of the function. y 3 x7
In Exercises find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x², (3,-4)
In Exercises use the rules of differentiation to find the derivative of the function. У 1 X
In Exercises find the slope of the tangent line to the graph of the function at the given point. g(x) = x² − 9, (2,-5)
In Exercises find the slope of the tangent line to the graph of the function at the given point. 3 g(x) = ¾¼x + 1, (−2, − 2)
In Exercises use the Product Rule to find the derivative of the function. f(x) = x³ cos x
In Exercises use the rules of differentiation to find the derivative of the function.y = x12
In Exercises use the graph shown in the figure. To print an enlarged copy of the graph.(a)(b) y 6 5 4 3 2 生 (4, 5) (1, 2) f H ++ 2 3 4 5 6 X
In Exercises use the rules of differentiation to find the derivative of the function.ƒ(x)= -9
In Exercises use the Product Rule to find the derivative of the function. (8 + 2) = (5)8
In Exercises use the graph shown in the figure. To print an enlarged copy of the graph.Identify or sketch each of the quantities on the figure.(a) ƒ(1) and ƒ(4)(b) ƒ(4) - ƒ(1)(c) 6 5 4 3 2 y (4, 5) (1, 2) f H 2 3 4 5 6
In Exercises use the Product Rule to find the derivative of the function. h(t) = √(1-1²)
In Exercises use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your answer analytically.(a)(b) y = x-1/2 y 2 (1, 1) 12 3 X
In Exercises use the rules of differentiation to find the derivative of the function.y = 12
In Exercises estimate the slope of the graph at the points (x1, y1) and (x2, y2). (¹x 4x) y NEXHI X
In Exercises use the Product Rule to find the derivative of the function. (3x − 4)(x³ + 5) - y = (3x
In Exercises use the graph toestimate the slope of the tangent line to y = xn at the point(1, 1). Verify your answer analytically.(a)(b) y = x¹/2 2 1 (1, 1) 1 2
In Exercises estimate the slope of the graph at the points (x1, y1) and (x2, y2). X # (²x Tx) # y (¹x 4x).
In Exercises use the Product Rule to find the derivative of the function. g(x) = (x² + 3)(x² − 4x)
In Exercises describe the interval(s) on which the function is continuous. f(x) = cos 1 X
Use the Intermediate Value Theorem to show that ƒ(x) = 2x³ - 3 hasa zero in the interval [1, 2].
Let P(x, y) be a point on the parabola y = x² in the first quadrant. Consider the triangle ΔPAO formed by P,A(0, 1), and the origin O(0, 0), and the triangle ΔPBO formedby P, B(1, 0), and the origin.(a) Write the perimeter of each triangle in terms of x.(b) Let r(x) be the ratio of the
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as approaches -2 from the left and from the right. f(x): = + H -2 2 1.x² 4 2 4 2 -2 X y - 24 X
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
Let P(x, y) be a point on the parabola y = x² in the first quadrant. Consider the triangle ΔPAO formed by P, A(0, 1),and the origin O(0, 0), and the triangle ΔPBO formed by P,B(1, 0), and the origin.(a) Write the area of each triangle in terms of x.(b) Let a(x) be the ratio of the areas of the
In Exercises determine whether the problem can be solved using precalculus or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical approach to estimate the
In exercises use a graphing utility to graph the function and visually estimate the limits.h(x) = -x² + 4xa.b. lim h(x)
(a) Find the area of a regular hexagon inscribed in a circle of radius 1. How close is this area to that of the circle?(b) Find the area An of an n-sided regular polygon inscribed in a circle of radius 1. Write your answer as a function of n.(c) Complete the table. What number does An approach as n
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as approaches -2 from the left and from the right. f(x) 1 x + 2 3 2 -1 -2 y -3- 1
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as approaches -2 from the left and from the right. ƒ(x) = tan 13 -6 -2 1 y TT.X 4 2 1+1 6 1 X
In exercises use a graphing utility to graph the function and visually estimate the limits.a.b. g(x) = 12(√√x - 3) x-9
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
In exercises use a graphing utility to graph the function and visually estimate the limits.ƒ(x) = x cos xa.b. lim f(x) x->0
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as approaches -2 from the left and from the right. f(x) = -6 = sec y Π.Χ. 4 2 nn 6 X
In Exercises complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. x - 3 lim x →3 x² = 7x + 12 X f(x) 2.9 2.99 2.999 3 ? 3.001 3.01 3.1
In Exercises determine whether the problem can be solved using precalculus or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical approach to estimate the
In exercises use a graphing utility to graph the function and visually estimate the limits.ƒ(t) = t |t - 4|a.b. lim f(t)
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches 4 from theleft and from the right. f(x) = = 1 x 4
In Exercises complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. lim x-0 X f(x) x +4-2 X -0.1 -0.01 -0.001 0 0. 0.001 0.01 ? 0.1
In Exercises use the graph to find the limit (if it exists). If the limit does not exist, explain why.a.b. h(x) = + y 4€ 3 2 4x - x² X + 1 2 3 4
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
In Exercises use the graph to determine the limit, and discuss the continuity of the function.a.b.c. lim f(x) x-c+
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches 4 from the left and from the right. f(x) = −1 x - 4
In Exercises determine whether ƒ(x) approaches ∞ or -∞ as x approaches 4 from the left and from the right. f(x) 1 (x-4)²
In Exercises use the graph to find the limit (if it exists). If the limit does not exist, explain why.a.b. g(x) = -3 9 6 3 - 2x x - 3 y -6 -9 + 36
Determine all values of the constant a such that the following function is continuous for all real numbers. f(x) = ax tan x la² - 2, 2, x ≥ 0 x < 0
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