Use the mean value theorem to prove the inequality for all a and b: Isina – sinb| < |a - b|.

Q: (4) Evaluate S SR e™y-2dA where R is the region enclosed by y = 4x, y = }, y = ± and y = 1.

A: Let's find.

Q: Solve the following differential equations: 1.) y’ = x2 A. y = x3/ 3  B. y = x2/ 3  C. y = x ln 3 D.…

A: Integrating both sides.

Q: 3x2 + 4x + 1 dx 2. 2x2

A:

Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

A:

Q: Find the vector

A: The vector r=&lt;a,b&gt; is written as, r(i)=ai+ bj

Q: dy 3. Find of the following equations: dx b. xy = 2x?y – 8x

A:

Q: 1. Find the derivative of the following: (Simplify your final answers.) sech h. j(r) = e (Using…

A:

Q: A mass weighing 16 pounds is attached to a spring whose spring constant is 25 lb/ft. What is the…

A: Given that, the mass weighing =16 pounds Now, changing the unit of the mass: m=1632=0.5 slug

Q: Question Suppose f is continuous on [3, 10] and differentiable on (3, 10). If 5 <f'(x) < 8 for all…

A:

Q: 4. Find all real values of x such that |x-1| : Ix+11. O (00,-1| O (00,0) O 1,0) O 1,1) None of the…

A: Given query is to find the value of x.

Q: 5. [4 log x + 1] dx

A: Student has specifically asked for the solution to the Question (5). Hence answer to that problem is…

Q: 3n-2 5. For the sequence an = 7+5n a. Find the limit if it exists. 3n-2 b. Does the series E-1…

A:

Q: Switch the order of integration for the double integral below and evaluate it. On your paper, sketch…

A:

Q: The height, h, in feet of an object launched straight up after t seconds can be represented by h(t)…

A:

Q: 1. Find the Fourier Transform of - 1 1 f(t) = -1

A: As per the guidelines I can solve only first question

Q: Approximate the local minimum value of the function given below. Use Newton's method with the…

A:

Q: ( + TO 1) y= sin 4. 6. 1 cos (20- TC %3D 2. 3

A:

Q: Find the inverse Laplace transform of 5s + 1 F(s) = s2 – 7s + 12

A: F(s)=5s+1s2-7s+12       =5s+1s2-3s-4s+12       =5s+1s(s-3)-4(s-3)       =21(s-3)-16(s-4)(s-3)(s-4)…

Q: B: .A card is drawn from a well shuffled pack of (iv) a card of diamond (v) a king or a queen

A:

Q: -3 -2 -1 1 2 4 8 16 32 64

A:

Q: Solve the equation with homogeneous coefficients. (3y² – x²)dx – 2xydy = 0

A:

Q: Given the rate law and table below, what are the values of m and n? Rate = k[A]m[B]" [A] (M) [B] (M)…

A: Given,

Q: A ball is thrown vertically upward from the top of the house 112 ft high with an initial velocity of…

A:

Q: Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures…

A:

Q: IV. Problem Solving: A. Write the expression as a single Integral. Choose your answer from the box.…

A: The given integral,∫02fxdx+∫23fxdx

Q: 5 ,2 X |x² + x – 6| dx -5

A:

Q: Directions: Solve the following using the theorems on differentiation. 1. Evaluate x5dx 2. Evaluate…

A:

Q: Let f be a function defined by f(x) = In(2x2 + 1) and let g be a function defined by g(x) = 2x4 –…

A:

Q: Diem 3. Sketch the region enclosed by the curves y = 2x, y = 2x², and find the area of that region.…

A:

Q: Radioactive Carbon-14 The percentage Pof radioactive carbon- 14 remaining in a fossil after t years…

A: Note: As P and b for the first question are not given in the data provided by you. Solved the second…

Q: 1. lim 32-3 +5 2. lim log, (x-8x 1) 3. lim (In 2x +5) + 4 Write your final answer using 4 decimals

A:

Q: A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if…

A:

Q: 14) Test the secies for convergane divergence or 2. (-1)"

A:

Q: 13. sec*0 sin 8 de

A:

Q: Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8…

A:

Q: 4- The number of element in the sample space when you flip 3 coins together c) 6 d) 12

A: We can solve this as follows:

Q: Region is bounded by y=x y=x2 Rotate about x=2. Find the area. Please help

A:

Q: dV = vt+1+t where V 4. The volume of a balloon is increasing according to the formula dt cm³ is the…

A: To solve the given differential equation and find an expression  for V(t).

Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

A:

Q: A line is parameterized by x = 5 + tand y = 6t. (a) What part of the line do we get by restricting t…

A:

Q: Let R be a variable and r a constant. Compute the derivative. d :(° · R') = dR

A:

Q: "If a function is continuous at some point then it must be differentiable at that point". Do you…

A: To show whether the given statement is true or false .

Q: Find the total area of the region between the x-axis and the graph of y = -x - 3x, - 6sxs1. The…

A:

Q: y' = xy – Vx

A: Solving

Q: Question 6 Use cylindrical shells to find the volume of the solid generated wher the region enclosed…

A:

Q: The evaluation of S S 3y³e*ydxdy is e - 1 O

A: Given: ∫01∫0y2 3y3exydxdy

Q: Answer the following questions; 1. A student writes that if the right and left limits of a function…

A:

Q: d. q(x) = cot-1 ( ) 1-nx

A: Follow the procedure given below.

Q: che unit sphere does the following in

A: We have to choose the correct option from the given options according to the given information