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study help
mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
Find the derivative of the function.f (x) = log2 3√2x + 1
Find an equation of the tangent line to the graph of the function at the given point.h(x) = -xe2-x, (2, -2)
Find the derivative of the function.y = log10 x2 - 1/x
Find the derivative of the function.f (x) = log2 x2/x - 1
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b).lim x 1+ (ln x)x-1
Find the extrema and points of inflection (if any exist) of the function. Use a graphing utility to graph the function and confirm your results.f (x) = (x + 1)e-x
Find the derivative of the function.g(x) = log5 4/x2√1 - x
Find the particular solution of the differential equation that satisfies the initial condition. dy dx 1 V4 - x2 y(0) = - 刀
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b). lim (x - √√√x² + 1) x 00
Find the particular solution of the differential equation that satisfies the initial condition. 1 4 + x² dy dx y(2) = π
Find the area of the given region. Use a graphing utility to verify your result. 2 1 1 x√√x² - 1 x= √2 1 2
Find the area of the given region. Use a graphing utility to verify your result. y + -2 2 4-x² y - 1 برا 3 2 1 2
Find the area of the given region. Use a graphing utility to verify your result. y 3 cos x 1 + sin²x 4 3, -2 -3+ X
Find the derivative of the function.f (t) = t3/2 log2 √t + 1
Find an equation of the tangent line to the graph of the function at the given point.y = 2-x, (-1, 2)
Find an equation of the tangent line to the graph of the function at the given point.y = 5x-2, (2, 1)
Find the area of the given region. Use a graphing utility to verify your result. y= -2 4e* 1 + ²x -I 3 -1 y x = ln √3 1 2 X
Find an equation of the tangent line to the graph of the function at the given point.y = log3 x, (27, 3)
Use logarithmic differentiation to find dy/dx.y = x2/x
Consider the function(a) Write a short paragraph giving a geometric interpretation of the function F(x) relative to the functionUse what you have written to guess the value of x that will make F maximum.(b) Perform the specified integration to find an alternative form of F(x). Use calculus to
(a) Show that(b) Approximate the number π by using the integration capabilities of a graphing utility. 4 1 + x² dx = 1.
Find the derivative of the function.y = cosh-1(3x)
Use logarithmic differentiation to find dy/dx.y = xx-1
Find the derivative of the function.y = csch-1(1 - x)
Find the derivative of the function.y = tanh-1√x
Evaluate the limit, using L’Hôpital’s Rule if necessary. I + 2x^ X lim
Find the derivative of the function.f (x) = coth-1(x2)
Evaluate the limit, using L’Hôpital’s Rule if necessary. घर e.x² %1-1³ lim X 00
Sketch the graph of the function.y = (1/4)x
Find the indefinite integral.∫3x dx
Find the derivative of the function.y = sinh-1(tan x)
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim x 00 COS X X
Find the indefinite integral.∫2-x dx
write the expression in algebraic form.sec(arctan 6x)
Find the derivative of the function.y = ln(tanh x/2)
Evaluate the limit, using L’Hôpital’s Rule if necessary. sin x 1 lim x ∞0 x X
Find the derivative of the function.h(t) = t/6 sinh(-3t)
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim 00 In x x²
Find the derivative of the function.y = (x2 + 1) coth x/3
Find the derivative of the function.y = e5x
Write the expression in algebraic form. cos(arcsin * = h) r
Find the derivative of the function.f (t) = arctan(sinh t)
(a) Find the inverse function of f, (b) Graph f and f-1 on the same set of coordinate axes,(c) Verify that f-1(f (x)) = x and f (f-1(x)) = x, and(d) State the domains and ranges of f and f-1.f (x) = 5x - 7
(a) Find the inverse function of f, (b) Graph f and f-1 on the same set of coordinate axes,(c) Verify that f-1(f (x)) = x and f (f-1(x)) = x, and(d) State the domains and ranges of f and f-1.f(x) = √x + 1
Find the derivative of the function.y = e-8x
Find the derivative of the function.g(x) = sech2 3x
Find or evaluate the integral by completing the square. 3 L₂= dx x² + 4x + 8
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim ∞o X² x4 x
Solve the equation accurate to three decimal places.log7 x3 = 1.9
Find or evaluate the integral by completing the square. dx -2x² + 8x + 4
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim x ∞ e²r-9 3x
Find the derivative of the function.y = e√x
Evaluate the limit, using L’Hôpital’s Rule if necessary. sin 5x lim x 0 tan 9x
Find an equation of the tangent line to the graph of the function at the given point.y = sinh(1 - x2), (1, 0)
Find or evaluate the integral by completing the square. dx 3x² - 6x + 12
Find an equation of the tangent line to the graph of the function at the given point.y = xcosh x, (1, 1)
Solve the equation for x.arcsin(3x - π) = 1/2
Find an equation of the tangent line to the graph of the function at the given point.y = esinh x, (0, 1)
Find the derivative of the function.f (x) = 4x
(a) Show that (23)2 ≠ 2(32).(b) Are f (x) = (xx)x and g(x) = x(xx) the same function? Why or why not?(c) Find f'(x) and g'(x).
The diagram shows a simple electric circuit consisting of a power source, a resistor, and an inductor. If voltage V is first applied at time t = 0, then the current I flowing through the circuit at time t is given by I = V/R (1 - e-Rt/L) where L is the inductance and R is the resistance. Use
Complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 4%Compounded continuously t P 1 10 20 30 40 50
Complete the table by determining the balance A for P dollars invested at rate r for t years and compounded n times per year.P = $7500r = 4.8%t = 30 years n A 1 2 4 12 365 Continuous Compounding
Complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 0.6%Compounded continuously t P 1 10 20 30 40 50
(a) A deposit of $550 is made in a savings account that pays an annual interest rate of 1% compounded monthly. What is the balance after 11 years?(b) How large a deposit, at 5% interest compounded continuously, must be made to obtain a balance of $10,000 in 15 years?(c) A deposit earns interest at
After t years, the value of a car purchased for $25,000 is V(t) = 25,000(3/4)t.(a) Use a graphing utility to graph the function and determine the value of the car 2 years after it was purchased.(b) Find the rates of change of V with respect to t when t = 1 and t = 4.(c) Use a graphing utility to
A geometric argument (see figure) was used to prove that(a) Write the area of ΔABD in terms of θ.(b) Write the area of the shaded region in terms of θ.(c) Write the ratio R of the area of ΔABD to that of the shaded region.(d) Find sin 8 lim во в = 1. =
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If p(x) is a polynomial, then lim p(x) ex = 0.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. x² + x + 1 lim- x 0 x lim x 0 2x + 1 1 1
The total numbers y of AIDS cases by year of diagnosis in Canada for the years 2005 through 2014 are shown in the table, with x = 5 corresponding to 2005.(a) Use the regression capabilities of a graphing utility to find the following models for the data.y1 = ax + by2 = a + b ln xy3 = abxy4 = axb(b)
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. f(x) If lim x 00 - g(x) = 1, then lim [f(x) g(x)] = 0. X 00
(a) Let f'(x) be continuous. Show that(b) Explain the result of part (a) graphically. lim h0 f(x+h)-f(xh) 2h = f'(x).
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.A limit of the form ∞/0 is indeterminate.
Let f''(x) be continuous. Show that f(x + h) − 2f(x) + f(x − h) h² lim h 0 = f"(x).
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.A limit of the form ∞ • ∞ is indeterminate.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.An indeterminate form does not guarantee the existence of a limit.
Find the derivative of the function.y = arccsc 2x2
Find the derivative of the function.y = 1/2 arctan e2x
Find the area of the given region. 6 y = 16+ x² 0.5 0.4 0.3 0.2+ 0.1 y TT T + + + 2 1 13 4 5 X
Evaluate 1.qx a* - 171/x a - 1 lim x ∞ X where a > 0, a 1. #
Verify the differentiation formula.d/dx [sech-1 x] = -1/x√1 - x2
Which is greaterwhere n > 8? (√√n)√"+1 or (√n + 1)√n
Find the exact value of the expression.51/ln 5
Find the exact value of the expression.6(ln 10)/ln 6
Find the exact value of the expression.91/ln 3
Find the exact value of the expression.321/ln 2
Let f (x) = ax -1/ax + 1 for a > 0, a ≠ 1. Show that f has an inverse function. Then find f-1.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. dx 25 + x² -18 || 25 arctan X 25 + C
(a) Determine y' given yx = xy.(b) Find the slope of the tangent line to the graph of yx = xy at each of the following points.(i) (c, c) (ii) (2, 4) (iii) (4, 2)(c) At what points on the graph of yx = xy does the tangent line not exist?
Find the derivative of the function.y = coth 8x2
Find the derivative of the function.y = ln(coth x)
The graph of g(x) = cos x is shown below. Explain whether the pointslie on the graph of y = arccos x. 1 2π (2). (a.) (0.7). 3 and (-1-3)
Find the derivative of the function.y = sinh-1(4x)
Find the derivative of the function.y = x tanh-1(2x)
Solve the equation accurate to three decimal places.41-x = 52
Find the derivative of the function.y = tanh-1(sin 2x)
Solve the equation accurate to three decimal places.2(3x+2) = 17
Find the indefinite integral.∫(x2 + 2-x) dx
Determine whether each inverse trigonometric function can be defined as shown. Explain.(a)(b) y = arcsec x, Domain: x > 1,Range: 2
Find the indefinite integral.∫(x4 + 5x) dx
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