Evaluate the following integrals (You need to show all your works) Question-1 (. 10 sinx (-2 cosx+2)dx%3D 0.

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m³/min. How fast is the...

A: Find your answer below 

Q: Given the matrix and its eigenvalues 2 27 0 0 4 40 has eigenvalues R, = 2 and R, = 34 and R, = 0 II ...

A: Solution is written in below steps.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it d...

A: We have to check weather the given Integral is converges or diverges.

Q: Question-2 (1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: For each function, determine whether it is a polynomial function. Is the function a polynomial? Func...

A: Check each function that it has positive integer powe of x or not in its each term. 

Q: 1. (a) Plot the first four terms of the sequence 3n2 — Зп + 2 2 n=1 (b) (i) Write in bracket notatio...

A: Please see the below picture for detailed solution. 

Q: Find the volume of the solid obtained by rotating the region bounded by 2y about the line x = – x = ...

A: NOTE: Refresh your page if you can't see any equations. .

Q: Suppose 135 small business firms are threatened by bankruptcy. If y is the number bankrupt by time t...

A:

Q: 3 situations that could represent functions

A:

Q: Differentiate the function. 1 g(x) 6 ,2 6x + 15 !! | g'(x) = %3D

A:

Q: For each function, determine whether it is a polynomial function. Is the function a polynomial? Func...

A:

Q: Consider the following. 2 + y- 16 (a) Find two explicit functions by solving the equation for y in t...

A: The objective is to solve the above questions. 

Q: Let the region R be the area enclosed by the function f(x) = x° + 2 and g(x) = 4x + 2. If the region...

A:

Q: x = 3 sin 0 is an appropriate trigonometric substitution for the integral 3-x2 dxp. x2 Select one: O...

A:

Q: Determine whether the improper integral diverges or converges. dx

A:

Q: Show the solution that a,+1 < a, for each n E N (-1)" п! n=1

A: Find your answer below 

Q: Find the radius of convergence and the interval of convergence. k + 2 Radius of convergence: 1 Inter...

A: To find the radius of convergence and interval of convergence use the following series tests. The c...

Q: A rectangular prism with dimensions 6 m × 4 m × 8 m (l×w ×h) is shrinking. (a)  Assume that the leng...

A:

Q: For each function, determine whether it is a polynomial function. Is the function a polynomial? Func...

A:

Q: For each function, determine whether it is a polynomial function. Is the function a polynomial? Func...

A: solution

Q: 00 (-1)"+l2nx" n² + 3 n=1

A:

Q: 2x x² – dx 2 — Зх — 10 3.x

A: Given ∫2x-3x2-3x-10dx We know that dxndx=nxn-1 Also, ∫1xdx = lnx+C

Q: I- dx et Р5+ 4e»

A: Explanation of the answer is as follows

Q: If f(x)= x³ -3x² +2x -1, then what is f' (-1)

A: f(x) = x3 -3x2 +2x -1 

Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx <2n? ...

A: We get the slope y' of the tangent to the function y=tan x-x by differentiating it with respect to x...

Q: Solve the area bounded by y³+y²+10 = (x+1)², the lines y=−2 and y=2

A: Given: - The curve is, y3+y2+10=(x+1)2 and the lines are y=-2 and y=2 To solve: - The area bounded b...

Q: Question Select your answer. What is the equation of the tangent line to the function 1 y = 2 1 I + ...

A: slop, and tangent line

Q: Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of...

A: We have to solve the question.

Q: Consider the function f(x) whose second derivative is f''(r) = 9x + 6 sin(z). If f(0) = 3 and f'(0) ...

A:

Q: If y=3xe , then what is d²y. 3x dx 2

A: Let's find. 

Q: consider the following  5^-x/50=9 a) find the exact solution of the exponential equation in terms ...

A:

Q: Consider the funetion 1) Find the domain of glx) 2) Find lim g(x) and limg(x). 3) Find oblique asymp...

A: Solution: Given data ,  g(x)= 2√(x2+3x)

Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros fo...

A:

Q: nctions f(x) = 3 + VI, 9(x) = x² – 3, %3D (a) (fo g)(x) (b) (go m)(r)

A:

Q: Consider the function F(x) = X-3sinx Find the indicoled limit 2'Hôpitel's Rulei slete thet it does n...

A:

Q: +3 dx 82x +3 (A) 2in(8) +C 82x +3 B +C In(8)2 82x+3 + C In(64) 42x +3 In(8) D - + C

A:

Q: Find if this series is convergent or divergent and provide detailed solution.

A: This question is related to infinite series, we will solve it using given information. 

Q: 3. Find the constant a so that o(x) = re2 is a solution to y+ay- e =0. 0 4 O 3 0 1

A: ϕ(x)=xe2x is a solution to y'+ay-e2x=0

Q: Differentiate the function. f(x) = log1,(x7 + 1) %3D f'(x) = %3D

A:

Q: f(x)=6x-10 , g(x)= x^2+3x+8 (gof)(-2) = 55 none of these 25

A:

Q: cossy sin³y dy 11. 1 а. 2 b.20 C. 20 d. none of the choices

A: ∫0π/2cos5y*sin5y dyWe know that cos2y=1-sin2y=∫cos(y)*sin5(y)(sin2(y)-1)2dy  Substitute u=sin(y)→dud...

Q: cos(x) = -7. Let g(x) = (x) sin(x) and h(x) =. x) Suppose = 2 and Find the following. (a) g g() = (a...

A: The given question has been solved in detail

Q: dy given that dx Use logarithmic differentiation to find sec-(T) 4sech(5z) (log6 x)" y =

A:

Q: (-1)"3nx" n² – 5 V. Determine the interval of convergence of > n=1

A: This is a problem of series calculation. By using concepts of series we will determine interval of c...

Q: Find the slope of the tangent line to the graph at the given point. (x2 + 4)y = 8, (-2, 1)

A: Slope = dy/dx

Q: Suppose that the equation of motion for a particle (where s is in meters and t in seconds) is 8 = si...

A:

Q: Let f(æ) = 9 sin(cos(x²)) || f' (x) =

A:

Q: Evaluate the integral -drz.

A:

Q: Problem 1. Let v = = (4, –2, -4) be a vector in R³. (a) Find a unit vector in the direction of v. (b...

A:

Q: 3. The Chain Rule. Solve Dx (2x2 + 2)* V2x CSC X

A: This is a problem of differentiation of the function. Based on below formula we will calculate the d...