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

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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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: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

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

A: Given         h(t)= t+51/3

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: x² F(x) = et dt

A: We will integrate the problem using fundamental theorem of calculus.

Q: f(x) = 'dt th (2) 3=

A:

Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

A:

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

A:

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: Differentiate f(x) with respect to g(x) of yx=xsiny

A:

Q: Differentiate. qx + r f(x) sx +t f '(x) = %3D (4'(x))(sx + t) + (s'(x))(gx +r) (sx + t)2

A: It is given that,   fx=qx+rsx+t We have to differentiate it.

Q: What is the local linearization of f(x) = near x = 1? NOTE: Enter your formula exactly, or round…

A:

Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

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

A:

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

A:

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: Find the general antiderivative of f(x) 3 – 4x* + - 5VT x3 Preview 2.

A:

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find f(x), the most general antiderivative of the function: f' (x) = 3x –

A:

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: 4. F(x) = (1- t) dt %3D 4

A:

Q: F(x) = f Cost dt 4

A: We need to evaluate F(x)=∫π4x2costdt. So,        F(x)=∫π4x2costdt      =sintπ4x2      =sinx2-12

Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: Find an antiderivative F(x) of f(x) = 7x – Vx.

A:

Q: Consider the function f(x) = 10x10 Enter the antiderivative of f(x) + 3x5 – 3x3 – 6. + C

A:

Q: Differentiate. f(x) = X + r SX +t

A: Given: fx=qx+rsx+t As we know that, The quotient rule: fg'=f'·g-f·g'g2 The Power law: ddxxn=nxn-1

Q: 6s-2 15. F(s): 2s²+4

A:

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

A:

Q: 3t dt g(x) g'(x) = ||

A:

Q: What is the antiderative of xysin((x^2)y)?

A:

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

A:

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the linear approximation of f(x) = Vx +I at a = 1.

A:

Q: Find the linearization of the function f(x)=x5 at x=1. L(x)= Using this linearlization, f(1.04).is…

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

A:

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

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: Find F'(x). 'x+7 F(x) = (6t + 7) dt %3D X1

A: Fundamental theorem of calculus If F(x)=∫af(x)g(t)dtThen,F'(x)=f'(x) g(f(x))

Q: Let F(x)= | V1+P dt. Find F'(5). x,

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Q: Differentiate the function. y=[(sx +2x+3) (x-3)]² dy dx II

A:

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: f(x) = Vx2 + xVx %3D

A:

Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

A:

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

A: Explanation of the answer is as follows