If f is continuous and f(x)dx=4, xf(x2)dx=

Q: 1. If f(x) cos(t) dt, then f'(x) =

A:

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

A:

Q: If f(x.y) = In(x² + y²) + find fr and fy -

A:

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

A:

Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

A:

Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

A:

Q: If f is continuous and q and h are differentiable functions, find a formula for d ch(x) f(t) dt dx…

A:

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: 9. Evaluate f, L" x²y²z dz dy dx ху Hw

A:

Q: Evaluate f S S," x dz dy dx

A:

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

A:

Q: If F(x,y) = ln (x²y – xy²), find Fy(3,2)

A: Given,   Fx,y=In x2y-xy2

Q: what is the derrivative of y^3 + y^2cos(x) = x^3 -3x and what points in the function for dy/dx does…

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: The total derivative of f(x,y) = e2x +5y is df =

A: Consider the following function: fx,y=e2x+5y Total derivative of function:…

Q: Let f(x) = 3x+ 4x. Evaluate dy when x=2 and dx=0.1

A: Given that fx=3x2+4x To evaluate dy when x = 2 and dx = 0.1.

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

A:

Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

A:

Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

A:

Q: Find all antiderivatives of function:  f (x) = e-3x

A: Consider the given function. fx=e-3x We have to find  I=∫e-3x dx   Substitute -3x=u -3dx=dudx=-du3

Q: 75. Show that (x – a)f(x) dx. f(t) dt ) dx

A:

Q: 11. Suppose | f(x) dx = 4, / f(x) dx = 5, and | f(x)dx = –1. Then f(x) dx = %3D %3D

A: The addition and subtraction property of integrals help to find the value of the given integral.…

Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

A:

Q: e If F(x) = | e dt, find F(1) and F'(x). ez

A:

Q: Let f(x) = 3x² + 4x. Evaluate dy when x=4 and dx=0.1

A:

Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

A:

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

A:

Q: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Let f(x) /1+ In (t) dt. 2 f(e) = D

A: Differentiate wrt x

Q: Let y = In(x'e2x ). Find dy/dx.

A:

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: If e**У- ху, then dx x(1- y) A Ax- 1) Ax - 1) B x(y- 1) (1- x) x(y- 1) x(y- 1) (D Ax - 1)

A:

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: If f(x) • g(x) is to be integrated with respect to x, taking dx as the differentiated variable,…

A:

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: If f f(x)dx si f(x)dx. 24. = 2; Sí f(x)dx = -1; ſ, f(x)dx = 7 , evaluate

A:

Q: Compute f -f(g(x)), where f(x) = x° and g(x) = 8x – 1. dx -f(g(x)) =| dx

A:

Q: 3 xf(x2)dx df(x) dx = -9, find If f is continuous and 0

A: f(x) is continuous

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

A:

Q: Find the 1st and 2nd derivatives of the following profit function: =(xa-110)1/a that is, and find…

A:

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

A:

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

A:

Q: Assuming that f(x) dx = 3, f(x) dx = 4, and f(x) dx = 8, calculate Fx) dx. %3D %3D Jo f(x) dx =

A: