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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises solve the differential equation. dy dx 1 80+ 8x 16x²
In Exercises solve the differential equation. dy dx x³ - 21x 5 + 4x - x²
In Exercises solve the differential equation. dy dx || 1 - 2x 4x- x²
In Exercises find the derivative of the function.y = sech(4x - 1)
In Exercises find the derivative of the function.y = coth(8x²)
In Exercises find the area of the region. y = sech 1.4 1.2 0.6 0.4 0.2 + 11 -4-3-2-1 y +11 1 2 3 4 - X
In Exercises find the derivative of the function.y = In(cosh x)
In Exercises find the indefinite integral. sech² x tanh x dx
In Exercises find the indefinite integral. S x² sech² x³ dx
In Exercises find the area of the region. y = tanh 2x -3 -2 I 3 2 1 نرا y -2- -3+ 1 2 3
In Exercises find the derivative of the function.y = sinh-¹(4x)
In Exercises find the indefinite integral. Is sinh 6x dx
In Exercises find the indefinite integral. Jese csch4(3x)coth(3x) dx
In Exercises find the area of the region. y= + 5x √x4 + 1 432 1 -4-3-2-1 -4 y 1 2 3 4 -X
In Exercises find the derivative of the function.y = xtanh-12r
In Exercises find the indefinite integral. 1 9 - 4x² dx
In Exercises find the area of the region. y -4 -2 6 - 4 y 8 6 2 -2 2 4 X
Chemicals A and B combine in a 3-to-1 ratio to form a compound. The amount of compound being produced at any time is proportional to the unchanged amounts of A and B remaining in the solution. So, when 3 kilograms of A is mixed with 2 kilograms of B, you haveOne kilogram of the compound is formed
In Exercises find the indefinite integral. X √√√x4-1 dx
Consider the equation of the tractrix(a) Find dy/dx.(b) Let L be the tangent line to the tractrix at the point P.When L intersects the y-axis at the point Q, show that thedistance between P and Q is a. y = a sech-¹(x/a) - √√a²-x², a > 0.
In Exercises verify the differentiation formula. d dx [cosh-¹x] = 1 x² - 1 ī
In Exercises find the indefinite integral. arcsin 2x 1-4x² dx
In Exercises find the indefinite integral. arctan(x/2) dx 4 + x²
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral. 1 x√√9x² - 49 dx
In Exercises find the indefinite integral. 1 3 + 25x2 dx
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral. X 1 - x4 dx
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
In Exercises find the indefinite integral. 1 e²x + e-2x dx
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
Exercises find the derivative of the function. y= x tanh 'x+Inv1 − 2
In Exercises find the derivative of the function. y = √√√x²-4-2 arcsec X 2² 2 < x < 4
In Exercises find the indefinite integral using the formulas from Theorem 5.2Data from in Theorem 5.2 THEOREM 5.2 Logarithmic Properties If a and b are positive numbers and n is rational, then the following properties are true. 1. In(1) = 0 2. In(ab) 3. In(a)= = In a + In b n In a a 4. In = In a -
Exercises find the derivative of the function. y = 2x sinh−'(2x) - √1 + 4x²
In Exercises find the derivative of the function. y = x(arcsin x)² - 2x + 2√√1-x² arcsin x
In Exercises find the derivative of the function. y = arctan e²x
In Exercises evaluate each expression without using a calculator.(a) tan(arccot 2)(b) cos(arcsec √√5)
In Exercises find the derivative of the function.y = x arcsec x
Exercises find the derivative of the function.y = sech-¹(cos 2x), 0 < x < π/4
In Exercises find the derivative of the function.y = arctan(2x² - 3)
Exercises find the derivative of the function.y = (csch-¹ x)²
In Exercises evaluate each expression without using a calculator.(a)(b) sin (arcsin)
In Exercises find the derivative of the function.y = tan(arcsin x)
Exercises find the derivative of the function.y = tanh -¹(sin 2x)
Exercises find the derivative of the function. y = tanh-1 t
Exercises find the derivative of the function. y = tanh-1 X 2
Exercises find the derivative of the function.y = sinh−1(tan x)
Exercises find the derivative of the function.ƒ(x)= coth-¹(x²)
(a) How large a deposit, at 5% interest compounded must be made to obtain a balance of $10,000 continuously, in 15 years?(b) A deposit earns interest at a rate of r percent compoundedcontinuously and doubles in value in 10 years. Find r.
In Exercises find the indefinite integral. 2-1/t 1² dt
In Exercises find the indefinite integral. fox. (x + 1)5(x + 1)² dx
In Exercises find the derivative of the function. g(x) = log, 1x
Use the graphs of ƒ and g shown in the figures to answer the following.(a) Identify the open interval(s) on which the graphs of ƒ and g are increasing or decreasing. (b) Identify the open interval(s) on which the graphs of ƒ and g are concave upward or concave downward. -2 T 3 2 a f(x) =
In Exercises find the derivative of the function. h(x) = logs X x-1
Exercises find the derivative of the function.y = cosh-¹(3x)
Which hyperbolic derivative formulas differ from their trigonometric counterparts by a minus sign?
In Exercises evaluate the integral. In 2 2ex cosh x dx
In Exercises evaluate the integral. 25x² dx
Which hyperbolic functions take on only positive values? Which hyperbolic functions are increasing on their domains?
In Exercises evaluate the integral. √√2/4 0 2 /1 - 4x² dx
In Exercises find the derivative of the function.ƒ(x) = x(4-3x)
Discuss several ways in which the hyperbolic functions are similar to the trigonometric functions.
In Exercises find the derivative of the function.y = x2x+1
In Exercises sketch the graph of the function by hand. y = (-) 4
In Exercises find the derivative of the function.ƒ(x) = 53x
In Exercises evaluate the integral. +4 1 25 - x² dx
In Exercises find the derivative of the function. g(x) = In ex 1 + ex
In Exercises evaluate the integral. So 10 cosh² x dx
In Exercises find the derivative of the function.ƒ(x) = 3x-1
In Exercises evaluate the integral. In 2 tanh x dx
In Exercises sketch the graph of the function by hand.y = 3x/2
The value V of an item t years after it is purchased is V = 9000e-0.6t for 0 ≤ t ≤ 5.(a) Use a graphing utility to graph the function.(b) Find the rates of change of V with respect to t when t = 1 and t = 4.(c) Use a graphing utility to graph the tangent lines to thefunction when t = 1 and t =
In Exercises use implicit differentiation to find dy/dx.cos x2 = xey
In Exercises find the indefinite integral. sech²(3x) dx
In Exercises find the indefinite integral. csch(1/x) coth(1/x) dx x²
Find the area of the region bounded by the graphs of y = 2e x, y = 0, x = 0, and x = 2.
In Exercises evaluate the definite integral. S₁² ex ex - 1 dx
In Exercises find the indefinite integral. I cosh x /9 – sinh? x dx
In Exercises find the indefinite integral. sech³ x tanh x dx
In Exercises evaluate the definite integral. 2 S = e2x e²x + 1 dx
In Exercises find the indefinite integral. x csch² -dx 2
In Exercises evaluate the definite integral. 5- xe-3x² dx
In Exercises find the indefinite integral. sech²(2x1) dx
In Exercises evaluate the definite integral. J1/2 el/x x² dx
In Exercises find the indefinite integral. e2r e²x - e-2x e²x + e-2x dx
In Exercises find the indefinite integral. sinh x 1 + sinh x - dx
In Exercises find the indefinite integral. [₁ x²ex³+1 dx
In Exercises find the indefinite integral. cosh x sinh x dx
In Exercises find the indefinite integral. cosh²(x - 1) sinh(x - 1) dx
In Exercises find the indefinite integral. e4x e2x + 1 ex dx
In Exercises find the indefinite integral. | xe!−xẻ dx xel-x²
In Exercises find the indefinite integral. cosh√√x √x dx
In Exercises find the indefinite integral. sinh(1 − 2x) dx
In Exercises find the indefinite integral. S cosh 2x dx
In Exercises a model for a power cable suspended between two towers is given. (a) Graph the model(b) Find the heights of the cable at the towers and at themidpoint between the towers(c) Find the slope of themodel at the point where the cable meets the right-hand tower. y = 10 + 15
In Exercises use implicit differentiation to find dy/dx.y ln x + y² = 0
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