2.x2 (а) lim,g->2 5x + 2 Зх — 6 а* (За — 1) (b) lim→∞ 50 + 4г — 2л3

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

A:

Q: The points P and Q have position vectors, relative to the origin O, given by OP = 7i + 7j - 5k and o...

A: We have to find equation of plane and distance AB

Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

A:

Q: A container with square base, vertical sides, and open top is to be made from 1000 ft2 of material....

A: Let the container has a base side "x" and height "y"

Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t – ...

A: topic - quadratic equations

Q: Explain why the integral is improper. 8. dx (x - 7)3/2 140 120 100 y 80- 60 40 20 O At least one of ...

A: Improper integral: If f(x) is continuous on the interval (a,b] and not continuous at x=a then,      ...

Q: Find the area of the surface obtained by rotating the curve y : sin x from x = 0 to x = 1.4 about th...

A: Given region bounded by y= sinx  from x=0 to x=1.4 

Q: 21 812 + 30t + 1 for t2 0, wheret is measured in 3 A train travels along a set of tracks according t...

A: Let's find. 

Q: Determine whether the improper integral diverges or converges. 00 dx 12 converges O diverges Evaluat...

A:

Q: Qal AIf fo =Sx-ul, gca)=x fin d fogcx) Then graph it determine domain and range.

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

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: I Find the second derivative (y") of the following functions and simplify the final results. 6. y = ...

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first...

Q: Watch help video Given the function f (x) = x + 6x² + 12x absolute minimum value of f on the closed ...

A:

Q: Standing on a level road 50 feet from the base of a billboard, the angle of inclination to the botto...

A:

Q: List down the steps in stimulating a secant method with explanation.

A:

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is th...

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the clos...

Q: 12 + csc 0[sin 0 + csc 0]d0

A:

Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to th...

A:

Q: Analyze ( find the relative extrema, inflection points) and trace the curve y = x3 - 3x2 - 9x + 5.

A: Given function f(x)=x3-3x2-9x+5

Q: Differentiate: -X=COS y O a. -sin y O b. -1/sin y O c. cSc y O d. secy

A: Topic:- derivative

Q: ſcos^3 (x) sin (x) dx, For the indicated integral, what would the first step be? * Add one to the po...

A: ∫cos3(x)sin(x)dx here we use substitute method so we have to substitute so lets substitute u = cosx

Q: Solve the differential equation by using integrating factors. y' = 6y + 5 y(x) =

A:

Q: +00 (2n)! E(-1)"- 2" n=1 O divergent O convergent

A: The objective is to find the convergence or divergence of the series. 

Q: Let f(x) = 9 cos(cos x) f'(x) =

A:

Q: (a) f(x)= Jx-6 (b) g(x)= /7-x (c) h(x)=V1-x²

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: 1. y = ax? + 2be2x

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y ...

A:

Q: CURRENT OBJECTIVE Calculate the derivative of an inverse function Question 4 2x Find (f-1)'(a) for f...

A:

Q: INTEGRATE THE FOLLOWING (use integration techniques) -2y dy 2. Sy'e-24 dy

A: topic- indefinite integral

Q: 3 2 y X-3x-x t3 From X = -1 to X= 8

A:

Q: 2. Use the sum and difference formulas to evaluate the following. 5TT COS 12 sin (-) 7Tt а. b. 12

A:

Q: Calculate the arc length of y = - x² - In x over the interval [1, 8e]. %3D

A:

Q: 17 Find the exact value of cos20 given csc0 and -< 0 < TI 8.

A:

Q: Find the exact value of cos20 given sin0 =- and 0 < 0 < 13

A:

Q: -6 -5 4 The plot above is created with the parametric equations S¤(t) = a cos(bt) y(t) = c sin(dt) T...

A: Solve the following

Q: Evaluate the following integrals |(6V - x-3)°dx

A: The integration of the integral is (6√x - x-3)2

Q: Solve the following equation on the interval [0,2n) V3cosecsce = 2cos0 b. 2 sin? x – 7sinx + 3 = 0 а...

A:

Q: d'y Find for x* +y* = 16. Express your answer in fully simplified form. dx?

A:

Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t)= t° – t² - 5t. D...

A:

Q: Find the expression of the general term of the sequence given by: 2 4 8 1, 2'6' 24' 120’ 720 16 32

A:

Q: Write the first-order differential equation in standard form. (Use yp for dy/dt.) dy dt = 7y + ty + ...

A:

Q: Solve the differential equation by using integrating factors. xy' = 3y + x2 y(x) =

A:

Q: (a) (6) Decide if the following improper integrals are convergent or divergent using Basic Compariso...

A: To decide the convergence of the improper integrals.

Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3 sin(x...

A:

Q: D. Evaluate the following limits by making a table of values for x. Consider 5 values of x for to es...

A: find limit

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

A:

Q: 1/2 dx r2)2

A: Given problem:-

Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

A:

Q: (cos v)³ + sin v dv (cos v)²

A: Topic:- integration

Q: Determine whether the improper integral diverges or converges. 1 dx e6x + e-6x converges O diverges ...

A: