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1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x (c) lim (* (d) lim ズ→1 Jx2+1 xー1

1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x (c) lim (* (d) lim ズ→1 Jx2+1 xー1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Evaluate the following limits (if it exists) Vx+6-x Vx3-1+x2-x (a) lim x-3 (b) lim ズ→1 ズー3 xー1 2x Vx2+1 (d) lim 2. (c) lim X→00 X1 Xー1 2. (a) Let f(x) = (x+1)(x³+x² +1)(x? -x+1) find f'(-1) X+1 Vx2+1 ex+2 (b) Let f (x) = x* , find f'(2) (c) Let g(x) = 2* , find g(5) (x) 3 Use the linear approximation to estimate the following numbers (a) In(0.97) (b) V7.94 (c) V10004 4. A deposit of $400 is made in an account that earns interest at an annual rate of 2.5%. How long will it take for the balance to double when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously? 5. Let f (x) = xVx² + 3 (a) Show that the function f (x) is one-to-one. (b) Find g'(f (-2)) for the function g(x) , that is the inverse function o-
Transcribed Image Text:1. Evaluate the following limits (if it exists) Vx+6-x Vx3-1+x2-x (a) lim x-3 (b) lim ズ→1 ズー3 xー1 2x Vx2+1 (d) lim 2. (c) lim X→00 X1 Xー1 2. (a) Let f(x) = (x+1)(x³+x² +1)(x? -x+1) find f'(-1) X+1 Vx2+1 ex+2 (b) Let f (x) = x* , find f'(2) (c) Let g(x) = 2* , find g(5) (x) 3 Use the linear approximation to estimate the following numbers (a) In(0.97) (b) V7.94 (c) V10004 4. A deposit of $400 is made in an account that earns interest at an annual rate of 2.5%. How long will it take for the balance to double when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously? 5. Let f (x) = xVx² + 3 (a) Show that the function f (x) is one-to-one. (b) Find g'(f (-2)) for the function g(x) , that is the inverse function o-
師簽 (r*)* -27 = 18 & 6. Suppose that f (x) is twice differentiable, lim ズ→1 ズ-1 s'(1+t)-f'(1-4t) lim = 1. Findf (1), f'(1), &f"(1). rectangular package to be by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 276 centimeters. Find the dimensions of the package with maximum volume. Assume that the package's dimensions are x by x by y (see figure). 7. 8 Determine the points where the tangent line to the curve of f(x) = x3 - 3x2 + 2 are parallel to the line y = 9x + 4 9. Given a normal probability density function f(x) = e z) , find out the inflection points and the maximum 1 ov2n 10. Sketch the graph of a rational function f (x) = 3ln(x² – 1) – 4x In the graph, you should discuss the domain of f and the concavity of f, describe the rise and fall of f, and find asymptotes, local minimum and maximum if they exist.
Transcribed Image Text:師簽 (r*)* -27 = 18 & 6. Suppose that f (x) is twice differentiable, lim ズ→1 ズ-1 s'(1+t)-f'(1-4t) lim = 1. Findf (1), f'(1), &f"(1). rectangular package to be by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 276 centimeters. Find the dimensions of the package with maximum volume. Assume that the package's dimensions are x by x by y (see figure). 7. 8 Determine the points where the tangent line to the curve of f(x) = x3 - 3x2 + 2 are parallel to the line y = 9x + 4 9. Given a normal probability density function f(x) = e z) , find out the inflection points and the maximum 1 ov2n 10. Sketch the graph of a rational function f (x) = 3ln(x² – 1) – 4x In the graph, you should discuss the domain of f and the concavity of f, describe the rise and fall of f, and find asymptotes, local minimum and maximum if they exist.
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