2. Suppose f(x) = g(3+3), and f'(x) = 13. What is the value of g(e)? (Hint:...
1. Suppose the a function g(x) is defined according to the formula f(c) 3(x + 2) +2 for – 3 <x< -2 (x+2)+1 for-2<x< -1 (+2)+1 for - 1<x<1 2 for r=1 for > 1 y 3+ 21 11 1 -2 1 2 (a) Compute f(a) for each of a = -2, -1,0,1,2. (b) Determine lim f(x) and lim f(x) for each of a = -2,-1,0,1,2. (c) Determine lim f(a) for each of a = -2,-1,0,1,2. If the limit fails...
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
6. Suppose the covariances between Xi and X2 is 3, between Xi and Xs is 2, and between X2 and X is 1. Moreover, the standard deviations of Xi, X2, Xs are, 3,2.2, respectively (a) Write the 3x3 covariance (2) and correlation (R) matrices of the random vectorX(X, X2, X). (b) Show that for any scalars aï.аг, аз: Var(aiX1 +a2X2 + asXs- (c) Use the formula in (b) and compute the (nunerical) value of Varlai XXaA) for the following choices...
5. Let f(x)- arctan(x) (a) (3 marks) Find the Taylor series about a 0 for f(x). Hint: - arctan(x) - dx You may assume that the Taylor series for f(x) converges to f (x) for values of x in the interval of convergence (b) (3 marks) What is the radius of convergence of the Taylor series for f(x)? Show that the Taylor series converges at x-1. (c) (3 marks) Hence, write T as a series (d) (3 marks) Go to...
5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error formula to a value of n so that |Mn (2) e10-4. You will likely want to use a calculator to determine the value of n. You might want to use the fact that e2 < 8 when working with the error formula. 5. Let Mn(x) be the nth Maclaurin polynomial for f(x) e as given in the text. Use the error...
The graph of f is shown to the right. The function F(x) is defined by for . a) Find F(0) and F(3). b) Find F'(1). c) For what value of x does F(x) have its maximum value? What is this maximum value? d) Sketch a possible graph of F. Do not attempt to find a formula for F. (You could, but it is more work than necessary.) We were unable to transcribe this imageWe were unable to transcribe this image9-3....
Your answer is incorrect. Try again. Let f(x) = g(h(x)) = (x - 7)3 + 2. Possible forms of g(x) and h(x) are O g(x) = x - 7, h(x) = x3 + 2. g(x) = x3 + 2, h(x) = x - 7. g(x) = (x - 7)3, n(x) = x - 2. g(x) = x - 2, h(x) = (x - 7)3. Click if you would like to Show Work for this question: Open Show Work x Incorrect....
·J (I) < 0 for all such y. (Hint: let g(x)--f(x) and use part (a)) 3. In this problem, we prove the Intermedinte Value Theorem. Let Intermediate Value Theorem. Let f : [a → R be continuous, and suppose f(a) < 0 and f(b) >0. Define S = {t E [a, b] : f(z) < 0 for allェE [a,t)) (a) Prove that s is nonempty and bounded above. Deduce that c= sup S exists, and that astst (b) Use Problem...
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use the following fact from single variable calculus: If f(x) g(x) for a KrS b, then (x)dJ() dr. Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that...
Contemporary Abstract Algebra 5. Suppose E is a field, F is a subfield E, and f(2),g(1) E FT with g2 +0. Show that if there exists h(1) E E[1] such that f(1) = g(2)h(1), then h(2) E FI:2 (i.c., if h(2) = Ek-141* € EU and f(1) = g(I)h(1), then as E F for 1 <k<n). Hint: One way to prove this is by using the division algorithm. Remark: This shows that if g(1) f(1) in E[L], then g(2) f(x)...