(4 points) Let f(x)--x-4-4 Find the value(s) of a that makes f continuous for all real numbers. if x#4 if x = 4 b. al (4 points) Let f(x)--x-4-4 Find the value(s) of a that makes f continuou...
Final page 5 of 13 4. Let f(x)8+1 a) Find all the critical points. b) Find the interval(s) where f(x) is decreasing. List these intervals c) Find the r coordinates of all relative maxima. d) Find, if they exist, the s-coordinates of all points of inflection e) Determine the intervals where f is concave up. List these intervals Final page 5 of 13 4. Let f(x)8+1 a) Find all the critical points. b) Find the interval(s) where f(x) is decreasing....
Let S the set of all points x+0 of RAn. Suppose that r=1x11 and be f a vector field defined in S by the equation f(x)=r^px Being p a real constant. Find a potencial function for f in S Let S the set of all points x+0 of RAn. Suppose that r=1x11 and be f a vector field defined in S by the equation f(x)=r^px Being p a real constant. Find a potencial function for f in S
Thanks for answering in advance. a, b Let f(x) be the |b al- 2. Let f(x be a continuous function defined on periodic extension of f. Find the Fourier coefficients of f in terms of integrals of f a, b Let f(x) be the |b al- 2. Let f(x be a continuous function defined on periodic extension of f. Find the Fourier coefficients of f in terms of integrals of f
Any help with work would be greatly appreciated. xf(x) f) f) f")f) 15 2 4 23 2 6. Let fbe a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above. (a) Write the second-degree Taylor polynomial for fabout x 0 and use it to approximate f(0.2) (b) Let g be a function such that g() ) Write the fifth-degree Taylor polynomial for g', the...
4. Let {S.} be a sequence of differentiable real-valued functions on (a, b) that converges pointwise to a function f on (a, b). Suppose the sequence {f) converges uniformly on every compact subset of (a, b). Prove thatf is differen- tiable on (a, b) and that f'(x) = lim f(x) for all x E (a, b). 4. Let {S.} be a sequence of differentiable real-valued functions on (a, b) that converges pointwise to a function f on (a, b). Suppose...
Question 4. (20 points) Let f : [a, bR be continuously differentiable (that is f'(x) erists and is a continuous function). For any partition Po,...,xn] of la, b] let TL Ti-1 3-1 and V(f)- sup V(f, P) | b P is a partition of a, Show that V(f)If' (x)dz Question 4. (20 points) Let f : [a, bR be continuously differentiable (that is f'(x) erists and is a continuous function). For any partition Po,...,xn] of la, b] let TL Ti-1...
6. (4 points) Show that f(x)= 1/x is not uniformly continuous on (0,1]. 7. (4 points) Show that t.-nlg(1+ 1n is convergent, and find the limit. To do this, apply Taylor's theorem, and use that (logr)'-1/ 6. (4 points) Show that f(x)= 1/x is not uniformly continuous on (0,1]. 7. (4 points) Show that t.-nlg(1+ 1n is convergent, and find the limit. To do this, apply Taylor's theorem, and use that (logr)'-1/
14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there have to be a local extrema on the graph of u = f(x) at x = c. 15. If/"(z) =-4(-7)2(z + 1) and the domain of f(x) is all real numbers, determine where f(x) is concave up, concave down and find any r-values of inflection points. 14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there...
Number 6 please S. Let ) be a sequence of continuous real-valued functions that converges uniformly to a function fon a set ECR. Prove that lim S.(z) =S(x) for every sequence (x.) C Esuch that ,E E 6. Let ECRand let D be a dense subset of E. If .) is a sequence of continuous real-valued functions on E. and if () converges unifomly on D. prove that (.) converges uniformly on E. (Recall that D is dense in E...
2. Let X be a continuous r.v. with pdf fx() for which EX exists. We want to find the real number a that minimizes EX-al over all real a. Determine an equation involving the CDF Fx(-) that can be solved to obtain a*. 2. Let X be a continuous r.v. with pdf fx() for which EX exists. We want to find the real number a that minimizes EX-al over all real a. Determine an equation involving the CDF Fx(-) that...