Q5: Find for the following functions: dx (1) In(x - y) = xy + y³;

Q: Using the Factor Theorem, which of the following is a factor of the polynomial function f(x) = 5x² +…

A: Given polynomial function is f(x)=5x3+5x2-60x

Q: [ 81e-9 sin 9xdx

A: Please see the below picture for detailed solution.

Q: For f(x) = 6x and g(x)=x+8, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.…

A: Solution ) f(x) = 6x , g(x) = x + 8  a) (f o g) ( x ) = f ( g(x) ) = f( x + 8 )  = 6 ( x + 8 )  = 6x…

Q: 2 Find the average rate of change of the function f(x) = x² + 7x from x₁ = 4 to x₂ = 5. The average…

A: Use average rate formula

Q: H.W: Evaluate the integral 30 J S (x²y- 0-2 1. (x²y - 2xy)dydx

A:

Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

Q: Q2: Solve the following in 7x²+14x+15 (1) f dx ; (x²+3)(x+7)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Given that, the position vector is rt=3t,4cost,4sint. Obtain the velocity.…

Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: Evaluate the function at the given values of the independent variables. Simplify the results. g(x,…

A: We can solve this as follows:

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y =…

A: y = x5 y =1  find V = ?   V = π∫(f(x))2dx here we have to find limit of x  here first quadrant given…

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

A:

Q: For f(x)= x+1 and g(x)= find X a. (fog)(x); b. the domain of fog a. (fog)(x) = (Simplify your…

A: The given functions fx=xx+1 and gx=11x

Q: Find the point (if it exists) at which the following plane and curve intersect. z = 19; r(t) = (t,…

A:

Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: S 2 (2x² + 1) dx

A:

Q: 2. What is the radius of the circle defined by x + y² - 6x + 4y - 1 = 0

A: x2 +y2 -6x +4y -1 = 0 here we have to find radius standrad form of circle is (x-a)2 + (y-b)2 = r2…

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A:

Q: 4. What is the length of the latus rectum of the ellipse whose equation is (x-3)² + 2 = 1. 25 16

A:

Q: What is the value of x if log, √x-1=2? O 82 65 O 19 0-8

A:

Q: The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = π. dA = ( A =…

A: Here is your solution

Q: Consider the three matrices A = (b) 2 -1 1 0 -1 2 94-1 B = 2 y and C = −1 multiplication is…

A: The objective of the question is determine sizes if possible and evaluate the values x,y and z.

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A:

Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z

A:

Q: Find the length of the following three-dimensional curv r(t) = (9+5t,3-2t,-1+2t), for 1sts6

A: To find the length of the given three dimensional curve.

Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: The line graph shows the average number of awakenings during the night for men and women of…

A: To find the difference between the average of awakening during the night.

Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

A:

Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7.

A: I have stated the used formulas in the solution

Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

A:

Q: nd the limit (if it exists). (If an answer does not exist, enter DNE.) 15 lim (x,y) → (0,0) x6y²

A: To  find the  limit.

Q: 28. For each of the following equations, find the most general function N(x, y) so that the equation…

A:

Q: Calculate the distance between the point Q(3, 1, 7) and the plane 2x - 6y – z = 3. Don't use a…

A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: A boat purchased for $25,000 depreciates exponentially. After one year, the car is valued at…

A:

Q: 61. A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R…

A:

Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

A:

Q: lf f(x) = -[-² 0 u²-6u +5du, then what is the y-coordinate of its inflection point? Selected Answer:…

A:

Q: Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity…

A:

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1

A:

Q: Q5: Find for the following functions: (4) y = x sinh 2x cosh 2x (3) y = e* sin² x In√x

A: The given functions,3) y=exsin2xlnx4) y=xsinh2x-12cosh2x

Q: Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then…

A:

Q: 9. -1 2x xe dx

A: We have to find out solution of integral

Q: Find the area of the region bounded by the cubic y= (x + 2)(x - 1)(x - 3) and the x-axis. Write your…

A:

Q: 2π π +][im [[(sinx + cosy)dxdy πο 5.

A:

Q: (-3,-2); find tan

A: tan = y/x tan = y component/x component  here  y = -2 x = -3

Q: A circular swimming pool has a diameter of 16 ft, the sides are 6 ft high, and the depth of the…

A:

Q: P 1. por Find a power series representation for the function f(x) = 92 and determine the radius of…

A: We have to find power series representation of given function and radius of convergence.

Q: (C): If w = tan x and x = 4²³ +t: Find?

A: