x* (x – 1)? (x + 2) (x² + 1)* Calculate the derivative by logarithmic differentiation: g(x)

Q: Find the first term and the common difference. 3 7 9. 2, - - 2' 4 ... 4 a, =], d=D %3D (Simplify…

A: Given query is to find the first term and common difference.

Q: 5. Evaluate each of the following integrals. (a) dr. (b) Vr2 +9 dx

A: LetI=∫x32x4+13dxPut 2x4+1=udifferentiate  on both side8x3dx=dux3dx=du8ThereforeI=∫1(u)3du8Take the…

Q: Given the vector field F = (z,x, y), calculate the flux of the curl of F through the portion of the…

A: Given

Q: Find the demand function p, given the marginal-revenue function dr/dq below. dr = 269 – 9q - 1.29 dq…

A: Here, the given marginal revenue function is: drdq=269-9q-1.2q2...(1) where r is the revenue…

Q: Given that lim f(x) = 0 x-a lim g(x) = 0 lim h(x) = 1 xa lim p(x) = 0 lim q(x) = 00, xa evaluate if…

A:

Q: 021 - In simpson's 1/3rule the intervals must be c) non of them [2 3 022- The eigin value of matrix…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

A:

Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: Determine which value best approximates the surface area of z = f(x, y) over the region R. (Make…

A: Given that the area of surface z = f(x,y) over the region. Let consider the given function, f(x,y) =…

Q: Find the derivative of the given function. dx %3D

A:

Q: 2) Find the absolute maximum and minimum values of f, if any, on the given interval, and state where…

A: We know that for absolute maxima and minimum value we do derivatives. We know that derivatives of…

Q: Find the solution of the following differential equation: y'' − 2y'= x − e3x

A:

Q: 1. x'-11/x +2 dx

A:

Q: Calculate the following limits. Justify your answer. (without using L'Hospital's rule Rule)

A:

Q: Find the limit. Use T Hospital s cos(x) lim - sin(x) + 1- x- (1/2) os (27) CoS sin(2n) 1- 0.

A: Given query is to find the limit of the expression.

Q: 7. Find the length of the curve y (r + 4)/2 on the interval [0,3] 8. Set up, but do not evaluate, an…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Use series to estimate the integral 1-cos x dx x2

A: Series

Q: Assume that all constants are positive and not equal to 1. 7" = 6 Hint

A: Given query is to find write the expression in logarithmic form.

Q: 1. Consider the graph of y f(z) below. State the value of each of the following. You do not need to…

A:

Q: Question 11 > A 25-year-old woman burns 400 – 70t cal/hr while walking on her treadmill. Her caloric…

A: We will integrate the given function

Q: 15 If f(x) 2 sin : then f'(x)

A: We will find f'(x) of the given function f(x)=2sin-1x5 in the following step.

Q: Find the slope of the tangent line to the curve - 32 + 2ry-y = 0 at the point ( 1, – 1).

A:

Q: An open-topped storage box with a square base has a capacity of 5 m3. The material for the sides…

A:

Q: ermine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

A: Given query is to find the infection point and interval of concave up and down.

Q: Find the indefinite integral. Hint: Let u = 3 - Vx. (Remember the constant of integration. Remember…

A:

Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

A:

Q: 12. Solve the second-Order differential equation: -y = e* (use method of variation of parameters)

A:

Q: When a drug is intravenously administered to a patient on a continuous basis, the amount A (in…

A:

Q: Find a gradient of the equation: F(x, y) = y + x³ – ay? + 3 %3D VF =?

A:

Q: A rectangular garden is to be fenced in next to a garage so that fencing is needed on three sides…

A: Let the dimension of the rectangular garden be:                             Length=L and Width=W…

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. x3 + y = 6xy…

A:

Q: What is the radius of an expanding circle at the moment when the rate of change of its area is…

A:

Q: The radius of a circle is to be measured and its area computed. The error in the measurement of the…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 1 to z = 6 using a Left Endpoint Approximate the area under the curve graphed below from z =…

A: Follow the procedure given below.

Q: Find the slope of the graph of the function y = 2x at (2,2) Then find an equation of the line…

A: We need to find slope and equation of tangent line.

Q: dy 3x2 + 2 and dt dx Find 3 if y = – 2. at x - dt dx dt

A:

Q: Q1\ Differentiate the following (choose two only) 1)z = sin (3x + 1) 2)f (x) = 3cot-12t 3)y = e 8*…

A:

Q: Find the equation of the tangent line to the curve g(x) = 4x² – 3x + 2 at the point (1, 3).

A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where; m is the…

Q: For problems 1 & 2 determine the length of the vector function on the give 1. ř (t) = (3 – 4t) i +…

A: First differentiate the given vector function and the find its norm and then find its length by…

Q: lim (4x - V16х? + 3х — 5 -Зх — 5 x00

A: Given :

Q: y(x) = (Simplify your answer. Do not factor.)

A:

Q: 2000 A television camera at ground level is 2000 feet away from the launching pad of a space rocket…

A: Rate of change

Q: e*i Ax lim Ei=11+xi [0, 1] 2) %3D1

A:

Q: Sketch the region from the first quadrant, bounded by y = 2x2, x = 0, and x- 2y + 3 = 0, and find…

A:

Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A:

Q: Determine the particular solution that satisfies the differential equation and initial condition…

A:

Q: Find the value V of the Riemann sum V = f(ck)A¤k k=1 for the function f(æ) = x² + 3 using the…

A:

Q: sin vn 2n Determine the convergence of the sequence an . If it converges, find lim an. BIU A E EV…

A:

Q: O Use polar coordinates to evaluate the integral V2² + y²dxdy. -V9-y2 got sdi wolod bas sitt od

A:

Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

A: