Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well defined. x +1 Let f(x) = and g(x) = x? +1. x +2' i. Find fog, gof. What are the domains and ranges of these functions? ii. Determine if ƒ and g are one to one or onto. iii. Determine if fog or gof are one to one or onto.

Q: Show that z*dz 0 for any integer k + 1 where C is given by y(0) Reio for 0 < 0 < 27. (7a) by showing…

A:

Q: Consider the functions z= -6 ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

A: The given functions are z = -6ex lny,  x = lnu cosv, and y = u sinv. (a) The objective is to express…

Q: Construct an antiderivative for each of the functions below. *An antiderivative for f is a function…

A:

Q: Consider the function below. z²+4 z-2i z # 2i f(z) = (3 + 4i z = 2i Is f(z) continuous at z = 2i? If…

A: Let's solve.

Q: Hello! What is the solution to this question? Thank you for your help! Have a nice day :)

A:

Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: Consider the function 2+2+z9-2ry+y if (r,y) # (0,0) f(1, y) = if (1, y) = (0,0). (a). Find and at…

A:

Q: a2f b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D f(x,y) = In/x2 +…

A: The first step inludes the  partial differentiation of the functions individually with respect to y…

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

A:

Q: 2 Consider the function f(x) - x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

A:

Q: Q2: Find dyidx for the following function:- (1) y = In(x + 4)-xtan (4) y =x*+1) (2) xy + x*y = x +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the piecewise-defined function f defined by S 7– 2x? if x >1 f(x) = 19 – 4x if x < 1 Find…

A: This means f(x) is continuous at x=1

Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

A:

Q: Find the local linear approximation of the function f(x) = /3+a at zo = 1, and use it to approximate…

A:

Q: Consider the function f(x)=3/x^2- 54x^5, x>0 Let f(x) be the antiderivative of (x) with f(1)=0.…

A:

Q: 19 Let y be a function such that y(1) , where Y (s) = L{y (t)}. If it is known - that: d ds s4…

A:

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

A:

Q: Let f(x) = x – x³ on [0, 1]. f(0) f(1) = Find c such that f'(c) = 0 or, if Rolle's Theorem does not…

A:

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) &gt; 0.

Q: Find the local linear approximation of the function f(x) = /1+ x at xo = 3, and use it to…

A:

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

A:

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find the local linear approximation of the function f(x) = V1 + x at xo = 3, and use it to…

A:

Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: Let y = f(x) be an positive increasing function defined for x > 0. The length of the curve described…

A: Given:         Length of curve y=f(x) is between x=0 and x=t is equal to14t4+t2+lnt+4+t2−ln2.

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Consider the function 23 – 3y if (x, y) # (0,0), f (x, y) = x² + y? if (x, y) = (0,0). Show that…

A:

Q: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…

A:

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

A:

Q: Calculate of of and for the function f(x, y) defined as : ax' dy sin (xy) 1 + y f(x, y) =

A:

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Find the linearization L(x) of f(x) = cot x at x = 4

A:

Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

A:

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

A:

Q: 1. Suppose that f(z) is analytic for lz <1 and sa Show that there is a constant c < 1 such that…

A: To prove the estimate for }f(z)| over the disc or radius r, center 0

Q: 9. Determine the analytic functions f = u+iv, for which u(x, y) = r³+rg(y), where g is a twice…

A: (9) To Find: The Analytic function f for which the real part is u(x,y)=x3+xg(y), where g is a twice…

Q: (a) Use the Chain rule to compute the derivative of g(x) = (1+x²)® [ set g(x) = h(k(x)) where h(z) =…

A:

Q: Suppose f is differentiable at a and f(a) + 0. (a) Prove |f| is differentiable at a by using that…

A:

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: Find the antiderivative  F of f that satisfies the givencondition. Check your answer by comparing…

A: Given- fx=5x4-2x3, F0=4. To find- The antiderivative  F of f that satisfies the given condition.…

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

A:

Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…