Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Question
Chapter 4.5, Problem 4C
(a)
To determine
To state: the fundamental theorem of calculus in its original form.
(b)
To determine
To state: the fundamental theorem f calculus in its alternative form.
(c)
To determine
To state: the fundamental theorem of calculus using indefinite integral.
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Exercise 11.3 A slope field is given for the equation y' = 4y+4.
(a) Sketch the particular solution that corresponds to y(0) = −2
(b) Find the constant solution
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(e) Verify these results using only the differential equation y' = 4y+4.
Chapter 4 Solutions
Calculus
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Prob. 52NFARCh. 4 - Prob. 53NFARCh. 4 - Prob. 54NFARCh. 4 - Prob. 1SCCh. 4 - Prob. 2SCCh. 4 - Prob. 3SCCh. 4 - Prob. 4SCCh. 4 - Prob. 5SCCh. 4 - Prob. 6SCCh. 4 - Prob. 7SCCh. 4 - Prob. 8SCCh. 4 - Prob. 9SCCh. 4 - Prob. 10SCCh. 4 - Prob. 11SCCh. 4 - Prob. 12SCCh. 4 - Prob. 13SCCh. 4 - Prob. 14SCCh. 4 - Prob. 15SCCh. 4 - Prob. 16SCCh. 4 - Prob. 17SCCh. 4 - Prob. 18SCCh. 4 - Prob. 19SCCh. 4 - Prob. 20SCCh. 4 - Prob. 21SCCh. 4 - Prob. 22SCCh. 4 - Prob. 23SCCh. 4 - Prob. 24SCCh. 4 - Prob. 25SCCh. 4 - Prob. 26SCCh. 4 - Prob. 27SCCh. 4 - Prob. 28SCCh. 4 - Prob. 29SCCh. 4 - Prob. 30SCCh. 4 - Prob. 31SCCh. 4 - Prob. 32SCCh. 4 - Prob. 33SCCh. 4 - Prob. 34SCCh. 4 - Prob. 35SCCh. 4 - Prob. 36SCCh. 4 - Prob. 37SCCh. 4 - Prob. 38SCCh. 4 - Prob. 39SCCh. 4 - Prob. 40SCCh. 4 - Prob. 41SCCh. 4 - Prob. 42SCCh. 4 - Prob. 43SCCh. 4 - Prob. 44SCCh. 4 - Prob. 45SCCh. 4 - Prob. 46SCCh. 4 - Prob. 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- A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.arrow_forwardThe graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…arrow_forwardA graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.arrow_forward
- Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars). R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20arrow_forwardDifferentiate the following functions. (a) y(x) = x³+6x² -3x+1 (b) f(x)=5x-3x (c) h(x) = sin(2x2)arrow_forwardx-4 For the function f(x): find f'(x), the third derivative of f, and f(4) (x), the fourth derivative of f. x+7arrow_forward
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