cx+a 8. Let f : R –→R be continuous. For a > 0, let g(x) | f(t) dt, x E R. Show g is differentiable, find g'(x). x-a

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

A:

Q: x² - y² z = g(x, y) = x² + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

A: Given function is z=gx,y=x5−y5x4+y4 for x,y≠0,00            for x,y=0,0. We have to check whether…

Q: Consider the function f(t, p) 3 (pе' +1—р)". a. Find an expression for f(t, p) and evaluate that…

A: Given that:f(t, p)=(pet+1-p)n

Q: Consider the function below. (x, y) = x²e^xy (a) Evaluate f(3, 0). (b) Find the domain of f. ORX (0,…

A:

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

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

Q: Find the numbers at which the function if a 2 I+1, f(1) = {2-1, %3D is continuous.

A: To find the points where f is continuous.

Q: Polynomial Function Leading Coefficient Degree y-intercept X-intercepts Sketch of the graph 1. y…

A:

Q: Let u(t) = (3,3tt) and v(t) = (3r, - 21,2). Compute the derivative of the following function. %3D…

A:

Q: Describe the x-values at which f is differentiable. f(x) = (x − 3)2/5

A: f is differentiable for those x-values at which f'(x) exists. Calculate f'(x) and find for what…

Q: y3 (x, y) # (0,0) (x, y) = (0,0) 1. Let f(x, y) = {x2+y2' (0, Is the functionf continuous at (0,0)?…

A:

Q: pose that the function f is continuous everywhere. Suppose that F is any antiderivative of f, and…

A: In this question, the concept of Integral is applied. Integration Integration is a method of…

Q: (H.W): Is this function

A: We have to check whether g:R-->R ,g(x)=x^2 subjective or not

Q: the guotient f(xth) f(a) where h is cortont.

A:

Q: Prove that for any function f : X → Y and for any subsets Y₁ and Y₂ of Y, ƒ¯¹(Y₁ NY₂) = ƒ¯¹(Y₁) Ñ…

A:

Q: Let F(x, y) =. Evaluate (31) F dr (1,0,0) O a. 9 + 3e3 8+ 3e3 С. 8— Зе3 O d. 10 – 3e3

A: We will use basic knowledge of vector calculus and integral calculus to answer this question.

Q: For each of the following sequences, if the divergence test applies, either state that lim an does…

A:

Q: Evaluate L.F. F. dr. F(x, y) = 9x1 + 4yj C:r(t) = tinh V4 L 1

A:

Q: Determine the set of points domains at which the function is continuous.  G(x,y)= 2x tan y

A: To Find: Set of points in domain at which the function 2x tany is continuous.

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: Consider the function: 3.3 x²+yⓇ 0 if (x, y) = (0,0) if (x, y) = (0,0) a - Determine if f is…

A: