Suppose that a) b) f(x, y) = [15x²y; 0

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: Show that the function f(z)= Im(z) is nowhere differentiable.

A:

Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y, (b) y/(x+y),…

A: The objective of the question is to find the probability density function (pdf) of three different…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: Let f e E(0, ox) and let a be a positive real number. Define the function fa as follows Sal) = {";…

A: Properties of Laplace transformation

Q: Given the functions fz) = 3* and g(x) = sin x, determine the domain of the combined function y=…

A:

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

Q: Compute fFdr, where F(x, y) = (5+27x², 2xy) and C is a line segment from (0, 0) to (1,2). (Use…

A:

Q: Find the local extrema points of the function f(x)=(x−a)ex, where a is an arbitrary real number.

A: Consider the function

Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

A:

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

A:

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

A:

Q: Let f(x.y) = In ( x2 + y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 6 O b.3 O. 7 O d. 8…

A:

Q: Let f (x) = 2x + 3. Compute R6 and L6 over [0, 3].

A:

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

A:

Q: Let f: Z → Z be defined by f(x) = x² + 1, and let C = {1,2,3}.

A:

Q: (x) - provided

A: To fill the given blanks.

Q: 5. Assume that V × F = V × G. What is the most general relationship between F and G ?

A: ∇ x F = ∇x G => ∇ x (F - G) = 0

Q: Find the standard factorization of the entire function f(z) = cosyz

A: Using the Euler's formula as, cosθ+isinθ=eiθcosθ-isinθ=e-iθ Now adding both the equations,…

Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: dy by definition for the following functions: d.x x +1 Exercises (20.1): Find 1) y = r + 3 2) y x -…

A: dydx of the given functions are solved below in each parts..

Q: fix+ h)-x) Compute (h 0) for the given function. f(x) =

A: Consider the function: fx=19x To calculate f (x+h), fx+h=19x+h

Q: 5) Find functions f and g so that f • g = H -3 H(x) = Vх — 2

A:

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

A: