9. f(x) = xe−2*, a = 0

Q: Find the derivative of cos-¹(sin x)

A:

Q: 1. Evaluate the given integral Q. √x²+1 (x - y² + 1) dy dx

A:

Q: From 7 consonants and 5 vowels, how many words can be formed consisting of different consonants and…

A:

Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

A:

Q: y' = X 2 h

A:

Q: A parabola has an equation of y-32= 0. Compute for the surface area of the solid generated by…

A: Given: y=3x12 At y=0, x=0 The surface area of the surface of revolution formed by revolving the…

Q: The are of the parabola y=x² from (1, 1) to (2, 4) is rotated about the y-axis. Find the area of the…

A: Let's find area of the resulting surface.

Q: Assume that f(x) = 5x + 2 and f is defined on [-1,5). Then f has an absolute maximum value at 5.…

A: In given problem since function f (x) = 5x+2 is defined only on [-1,5) i.e. 5 is not in the domain…

Q: Find dy dx If y = 1- t² and x = 4+²

A:

Q: A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions of the can,…

A: Given problem:- A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions…

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: A right circular cone has a constant height of 10 m. Find the rate of change of its volume with…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx,…

A:

Q: dy dx X2 (1+y2)

A: Let's solve given diffrential equation.

Q: 4. Given that f'(x) = −6x² + x + 12 and f(1) = 7, find f(x).

A: Given : f'(x)=-6x2+x+12f(1)=7   To Find : f(x)

Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

A:

Q: Find the area under a curve whose equation is y = x³-3x²-x+3 From x = 0 to x = 2

A:

Q: The average value of f(x, y) over the rectangle R = {(x, y) | a ≤ x ≤ b, c ≤ y ≤d} is 1 fave = (b −…

A: The average value of a function f(x,y)  over  R={(x,y): a≤x≤b,  c≤y≤d}is given by1(b-a)(d-c) ∬R…

Q: 9. Find the family of the curve whose slope at any point is V√x + √x and also the member which…

A:

Q: -3x² - 4x + 3 1 x (x + 1)² dx

A: Given problem:-

Q: The displacement d (in meters) of an object at time t (in seconds) is given by the following…

A: This is a problem related to harmonic motion. Based on the general formula and concepts we will…

Q: a. lim+ 2x 3x²

A:

Q: M8 1 Σ n=1 h n’ + 8 +8 3

A:

Q: FIND THE AREA OF THE REGION BOUNDED BY THE FOLLOWING CURVES: 1. y = x(x-3), x = 0, x = 5 2. y =…

A: Given

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: f cot x dx Select one: a. In sina+c + c + c + c O b. In sec x oc. In csc r od. In cos x

A: cotx = cosx/sinx

Q: Evaluate the following limits. a. limx→+ 2x 3x²

A: This question is based on limits.

Q: [x³√₁-x² 2

A: ∫x31-x2dx=∫1-x2x3dx Let 1-x2=t⇒-2xdx=dt⇒xdx=-dt2                         =-∫(1-t)tdt2=-12∫(1-t)tdt…

Q: √² (5x²-3x+18) dx 9x - x³

A: Integration is done by dividing polynomial.

Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

A:

Q: The entire graph of the function h is shown in the figure below. Write the domain and range of h as…

A: Given query is to find the domain and range of the function.

Q: 10. f(x) = x³ + 1

A: Here, the given function is: f(x)=x3+1 Here, the y-intercept is (0,1) and no x-intercept is (-1,0)…

Q: Determine whether the following statements are True or False? y = f(x) 2 X (a) lim f(x) = 1 (b) lim…

A: Diagram is given. Determine whether the following statements are true or false

Q: From a certain instant, a right circular cylinder has a radius of 10 cm and altitude of 15 cm.  At…

A: This question is related to rate of change, we will solve it using given information.

Q: Find the second derivative of f(t) = [(1 + 3)¯¹ + 1]¯¹

A:

Q: In5 x ,2 limx→+00

A:

Q: -1 √₂² (3+2u) du -2

A:

Q: A plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4). Find a vector perpendicular…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 10300 cubic centimeters per min at the…

A:

Q: dx 1. S √3x²–2x+1 2 2. √₁² √√x² - 4x + 8

A:

Q: 1. Evaluate the given integral Q. Q - CC² LL- (x - y) dx dy y²

A:

Q: 2.1 Limits 2 1. Use the graph to estimate the limits or explain why the limits do not exist. y (a)…

A:

Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: Find the inverse of the function on the given domain. f(x) = (x−5)^2, [5,∞)

A:

Q: 5x=2 5. Find the member of the curve whose slope at any point is y+s point (3, 2) and passes through…

A:

Q: Topic: Area of Surface of Revolution The arc of the parabola y=x^2 from (1,1) to (2,4) is rotated…

A: We have to find the surface area.

Q: 1. F(s) = 4s+2 s²+6s+34

A:

Q: There are five men and three women in a room. How many committees of 4 people can be chosen from the…

A:

Q: X f(x) =< Q 14/15 7 x + 1 3 ;0≤x≤2 ;2≤ x ≤3 5 Tov Then what is the result of 3 (fx) dx 1

A:

Q: dy Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dx…

A: