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- 1. If f(x) is a function such that f(1) = 2, f(n + 1) = (3f(n)+1)/3 for n = 1, 2, 3, ..., what is the value of f(100)?arrow_forward== 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = .. f(n-1)(a) = 0, g(a) = g'(a) = ... = g(n-1)(a) = 0, and either f(n) (a) #0 or g(n) (a) #0 (or both); then f(x) lim: x→a g(x) ∞ f(n) (a) g(n) (a) if g(n)(a) = 0, otherwise. (Suggestion: Use Taylor's formula with Lagrange's form of the remainder, for both f(a+Ax) and g(a + Ax).)arrow_forward(x + 2 if x > 10 lx – 7 if x < 10’ D. ! ! Given f (x) = determine each of the following. a.) f(14) b.) f(10) c.) f(-1)arrow_forward
- 4. Let f(x) = (6x – 1 if x 0* Find the indicated function values. (a) f(-3) (b) f (0) (c) f(4)arrow_forwardLet h(r) = r³e=' – k6*. Find (h(x)) where k is a real number (i.e. k is a constant). drarrow_forwardSuppose that the functions q and r are defined as follows. q (x) = x²+7 r(x) = /x+8 Find the following. (a • r)(!) = 0 (r • 9)(1) = 0 ? %3!arrow_forward
- If f be the function defined by f (x) = x³ + x. If g (x) = f-¹ (x) and g (2) is the value of g' (2)? O 1 13 4 TH 1 = 1, whatarrow_forward10)arrow_forwardIf a function h satisfies h(-x) = h(x) for every number x in its domain, then h is called an even function. If h satisfies h(-x) = -h(x) for every number x in its domain, then h is called an odd function. Suppose that sh(x) dx = Answer the following: −1 and ſ³ h(x)dx = 2 -3 A. Suppose that h is an even function. Evaluate ſ³, h(x)dx. B. Suppose that h is an odd function. Evaluate ſ³, h(x)dx. C. Evaluate (2h(x) + 1)dx. D. Evaluate fh(x + 1)dx.arrow_forward
- Let n be a positive integer. Define the function fn (2) by dzn (2² Find the value of f(-1 + i). fn(z) = + 2x + 2)".arrow_forwardSuppose that f is a function with f'(2) = −5. If u is very very close to 0, then f(2 + u) is approximately(a) f(2) − 5 + u (b) f(2) + 5u (c) f(2) − 5 − u (d) f(2) − 5u (e) none of thesearrow_forwardIf f(x) = (3x – 2)(2x + 3), then a. f( – 2) = b. f'( – 2) = c. f''(– 2) = d. The values of x for which f(x) = 0 are Preview Preview e. The values of x for which f'(x) = 0 are Previewarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage