Consider the graph of the function f(x) given on the next page, which consists of line segments and a semi-circle. What is the area under the graph of f(x) on [0,5]? What is the average value of f(x) on [0,5]

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

A:

Q: e (5-x) dx = xydy

A:

Q: Find a power series representation for the function. f(x) = X 8 - x³

A:

Q: Compute the curl of the following vector field. F = (4x²-3y²,5xy,5z)

A: We have to find out solution

Q: 1. / (1 + 3x) dx 5 2. / u² (4 + u°) ³ du

A:

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

A: We have to find the dydx of the given function.

Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: Find the critical points of the given function. 1 a) f(x) = -√24/3+2¹/ +2-2/3

A: Since multiple questions are asked, I am answering first question

Q: 38.Calculate the surface area of the surface obtained by revolving the curve y = √9-x² around the…

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

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

A: Given:

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: Use L'Hopital's to determine the limit. lim 0 0 1 1-cos x I O sin x COS X as x approaches 0

A:

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Approximate the area of the region bounded by the graph of f(t) = cos (t/2/2) and the t-axis on…

A:

Q: C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

A:

Q: Use implicit differentiation for x² + y² O x/y O 5x O-x/y O -5x = 25.

A: To find the derivative.

Q: If y₁ and y2 are linearly independent solutions of ty" + 4y' + te³y = 0 and if W(y₁, y2)(1) = 4,…

A: Need to find out the Wy1,y24

Q: S 2 (2x² + 1) dx

A:

Q: Find dy x 3 In (x - y) = xy + y²

A:

Q: Find the limit as x approaches 3 for x²-3x 2x²-5x-3

A:

Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

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: J 24 tan3 xdx

A: topic- indefinite integral

Q: -2- 0 y = g(x) 4 7 x

A: To evaluate the integral.

Q: 62. y + y = 22 +10x X

A: To find out the general solution of the differential equation.

Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.

Q: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

A:

Q: Use L'Hopital's to determine the limit. lim Oo O1 ○ -1 enx ~|-1 as x approaches co

A: This question can be solved using the concept of L' Hopital's Rule and derivatives.

Q: Find three mutually orthogonal unit vectors in R³ besides ti, tj, and tk There are multiple ways to…

A:

Q: Prove that (3-2)(x+2) = 3+2i ifitues.

A:

Q: Solve the following differential equations: (1+x²) (dy-dx)=2xy dx

A:

Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = = How does the…

A: We have to find the solution of given initial value problem.

Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A: Find determinant of coefficient Matrix  Then find delta x ,delta y, delta z

Q: Find the average value of f(x) = -x+1 x3 Submit an exact answer using fractions and/or roots if…

A: The given function is;  f(x)=(-x+1)/x3 over the interval [-3,-1].

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

A:

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

A: We can find the tangent equation at the given point as below.

Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

A:

Q: Find S н - 2+ dx

A:

Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ca as…

A: find the general solution of differential equation y"-10y'+61y=0

Q: Use the figure below to find the exact value of the trigonometric function of angle A. csc (A) 7 5 A

A: We have to find the exact value of the trignometric angle A, csc(A)=? Since ABC is right triangle,…

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1…

A:

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

A:

Q: ( 1-x+zy) . ول دل ران 3(x+2y)

A:

Q: Use the graph below to answer the following questions. f(c) -6 -4 5 14- 12 10- 8 6- 4 2- 2 -4- -6-…

A:

Q: 7√2 2 0 x² 49-x² dxl

A: The given integral,        ∫0722x249-x2dx

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given Graphs y=x2-3xy=x3+x2-12x First we find point of intersection of graphs…

Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: The objective of the question is determine the orthogonal curve for the given curve.

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

A:

Q: (B): If A = 2i + 3j-4k; B = 3i-4j+ 5k and C = i + j-k, find: (iv) (3A + 4B). C (1) A.B (U) B.C (iii)…

A: