1. Show that function f(x)=D|x | is not differentiable at 0

Q: Verify that the function ƒ(x) = x4 is concave up for x > 0and for x < 0. Is x = 0 an…

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Q: H.W Is f (x) = x. |x| differentiable function? %3D

A: To find  f(x)=x|x| is differentiable function or not.

Q: 2 csc x 11. Evaluate dx by using substitution method. (1– cot x)'

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Q: Show that the following function is nowhere analytic. f(2) = 2xy + i(x² – y³) %3D

A: Function is said to be analytic at a point if there is a nbd of the point such that f is…

Q: Scx? + bx, 3 — х, x > 1 f (x) = X < 1

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Q: 1. Decide if there is an analytic function f (x + iy) whose real part satisfies Re(f) = xe".|

A: Given problem: To decide analytic function fx+iy whose real part satisfies Ref=xey.

Q: Which of the following functions is differentiable for all values of x? a. fAx) = 2r' + 5x² b.…

A: Given problem:-

Q: Let F(s)= [f(x-s)d. Find F(s) for the function f(x)= x", where n is a constant.

A: The power rule for integration is ∫x5dx=x66+C. Here, C is the constant and x is the integration…

Q: Let the function f(x) be given as follows: ax + b, x<1 f(x) = ; lt +x + 1, x 21 Employ appropriate…

A: is differentiable. Therefore, we have, RHD=LHD=f(x) Now,

Q: Is f(x) = x |x| differentiable at x = 0? Provide a brief justification of your answer.

A: First it needs to be proved that fx=xx is continuous at x=0 limx→0-fx=limx→0xx=limx→0-x2=0…

Q: Find the values of c and d that make the function 6x if x 2 continuous. с — d =

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Q: 2. Check the following function f(z) = iz – 37 is analytic or not (Use C.R equations).

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