(v) div(ƒÃ) = f div Ã+ grad(f).Ã

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: f(x) = xe (1+e*)

A:

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: Find the function y(x) satisfying dx2 = 12 - 12x, y'(0) = 5, and y(0) = 8. ay = 12- 12x, y'(0) = 5,…

A: an initial value problem  is an ordinary differential equation together with an initial condition…

Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

A:

Q: af Find of f (4.v) = sin ) 1+ y

A:

Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: df Use derivative rules to compute where f(x) = -2xe". dx x%3DIn 7

A:

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

A:

Q: X >0, for continious f functHon Sft)dt = xarctanx fla)=?

A:

Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

A:

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: Find the domain and range of the function f(x, y) = exy

A: Given information: The function fx,y=exy

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: 2. f(t) = -3t – 10

A: To find Laplace transform of given function we use the formula of Laplace transform.

Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

A:

Q: Determine the value of fr at (1, – 1) when f(x, y) = 3x + 2xy? – 2x²y + 4x.

A: Our Aim is to determine the value of fx at (1,-1) whenf(x,y)=3x3+2xy2-2x2y+4x -(i)

Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

A:

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

A:

Q: Fill in the blank. = F(s - a) whereas L eat dt F(s - a) =

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Evaluate dy for f(x)= (square root of x) +3 where x=9 and dx=0.12

A:

Q: rsin 28x /ī+ t² dt and If f (x) = So g (y) = ' f (x) dæ., what is g" (6s )? 168

A:

Q: 6s-2 15. F(s): 2s²+4

A:

Q: 8(x) = [f(t) dt.

A: To find all x-values in the interval -5<x<5 at which g has a critical point.Classify each…

Q: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

A:

Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Let f (2) = – z). (7z+ 10) (i

A:

Q: f(x)=Vx+10 X-4 Damain af flxt Donain of fle(x)) =

A:

Q: Find the average rate of change of the function f(x) = 2x- 4x 8, on the interval r E [-3,2]. |3D

A:

Q: The antiderivative of the function f(2) +7z is

A:

Q: Find the antiderivative of the function: f(x) = ex + 3x - x2

A:

Q: Is g(x) = Vx + 1 differentiable or not? Justify.

A: Note :-  f(x) is exist only if f(x)≥0.

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

A:

Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

A:

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: Find the third derivative of f (z) = T2x +I. fll! (z) =

A: Explanation of the answer is as follows

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.