Whether the statement “If
Answer to Problem 1PT
The given statement is
Explanation of Solution
The given statement is, “If
Equivalently if
The following example disproves the given statement.
Consider the derivative function
On comparing this with the given statement, it is obtained that, the function is
Compute the value of
Thus, the value of
Now find the value of
Thus, the value of
Clearly, it is observed that
Therefore, the given statement is
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Chapter 4 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
- Find constants c1 and c2 such that: G(x) = c1xe^−x + c2e^−x is an antiderivative of g(x) = 3xe^−x. answer using: A function F is an antiderivative of f if F′(x) = f(x).arrow_forwardLet be a derivable function and h (x) = g (x2 +1). Calculate h '(1) if g' (2) = 5.arrow_forwardFind an antiderivative of the function. (a) h(q) = sin(9) H(q) (b) f(x) = 3e* F(x) =arrow_forward
- Find the linearization of f (x) = xe-* at a = 0. (Hint: Remember the product rule.) OL(x) = 0 OL(x) = = -x O L(x) = 1 O L(x) = xarrow_forwardSuppose that F(x)=−4x^3 is an antiderivative of f(x) and G(x)=3x^3 is an antiderivative of g(x). Find ∫(f(x)+g(x))dx.arrow_forwardLet f(x) = (h(q(x)))P(=) where h, q and p are differentiable positive functions. Find f'(x).arrow_forward
- Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x). In all cases, a, b, c are real constants, and y is a function of x.arrow_forwardIf two functions F and G are both antiderivative of the function f then F(x) = G(x). (A) True B) Falsearrow_forwardFind antiderivative of f(x) = cosxarrow_forward
- Find the antiderivative of the function f(x) = x7. That is, find a function F(x) for which F'(x) = f(x). Use a capital "C" for any constant term. F(x)arrow_forwardFind an antiderivative F(x) of the function f(x) = (8sinx) / (13 + cosx) such that F(0) = 1.arrow_forwardV4 + 3f(x), where f(1) = 7 and f'(1) = 4, 62. If h(x) find h'(1).arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,