CALCULUS SINGLE VAR W/ACCESS >CI<
8th Edition
ISBN: 9781305764583
Author: Stewart
Publisher: CENGAGE C
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Chapter T, Problem 4CDT
(a)
To determine
To find: The process to find the function
(b)
To determine
To find: The process to find the function
(c)
To determine
To find: The process to find the function
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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
1. Compute
Lo
F⚫dr, where
and C is defined by
F(x, y) = (x² + y)i + (y − x)j
r(t) = (12t)i + (1 − 4t + 4t²)j
from the point (1, 1) to the origin.
2. Consider the vector force: F(x, y, z) = 2xye²i + (x²e² + y)j + (x²ye² — z)k.
(A) [80%] Show that F satisfies the conditions for a conservative vector field, and find a potential
function (x, y, z) for F. Remark: To find o, you must use the method explained in the
lecture.
(B) [20%] Use the Fundamental Theorem for Line Integrals to compute the work done by F on
an object moves along any path from (0,1,2) to (2, 1, -8).
Chapter T Solutions
CALCULUS SINGLE VAR W/ACCESS >CI<
Ch. T - Evaluate each expression without using a...Ch. T - Simplify each expression. Write your answer...Ch. T - Expand and simplify. (a) 3(x + 6) + 4(2x 5) (b)...Ch. T - Factor each expression. (a) 4x2 25 (b) 2x2 + 5x ...Ch. T - Simplify the rational expression. (a) x2+3x+2x2x2...Ch. T - Rationalize the expression and simplify. (a) 1052...Ch. T - Rewrite by completing the square. (a) x2 + x + 1...Ch. T - Solve the equation. (Find only the real...Ch. T - Solve each inequality. Write your answer using...Ch. T - State whether each equation is true or false. (a)...
Ch. T - Find an equation for the line that passes through...Ch. T - Prob. 2BDTCh. T - Prob. 3BDTCh. T - Prob. 4BDTCh. T - Sketch the region in the xy-plane defined by the...Ch. T - FIGURE FOR PROBLEM 1 1. The graph of a function f...Ch. T - If f(x) = x3, evaluate the difference quotient...Ch. T - Find the domain of the function. (a)...Ch. T - Prob. 4CDTCh. T - Without using a calculator, make a rough sketch of...Ch. T - Prob. 6CDTCh. T - If f(x) = x2 + 2x 1 and g(x) = 2x 3, find each...Ch. T - Convert from degrees to radians. (a) 300 (b) 18Ch. T - Convert from radians to degrees. (a) 5/6 (b) 2Ch. T - Find the length of an arc of a circle with radius...Ch. T - Prob. 4DDTCh. T - Express the lengths a and b in the figure in terms...Ch. T - If sinx=13 and secy=54, where x and y lie between...Ch. T - Prove the identities. (a) tan sin + cos = sec ...Ch. T - Prob. 8DDTCh. T - Sketch the graph of the function y = 1 + sin 2x...
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