x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C Option 1 Option 2 Inlx - 1 + Inlx + 1| -Inlx+ 31 + C In/x- 11+ Inx+ 11- 3. Inlx - 1| + Inlx + 1| +Injx + 3| + C Option 3 Option 4

Q: Answer the following questions for the function f(x) = a/a? defined on the interval -4 < x < 5. x+16…

A: We need to find concavity and inflection points.

Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

A:

Q: 4. By implicit differentiation , find the 1st derivative of x3 + y3 + 6xy = 0

A:

Q: tanode B В sec®

A:

Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: x2 - 8 R2.1 J x2 + 5x + 6 Answer with text and/or attachments

A:

Q: 5. Find the general solution: 9y" + 12y' + 4y = 0.

A:

Q: Which of the following is an antiderivative of f(x) = sin x cos x? %3D (a) sin²x (b) cos² ¤ sin 2x…

A: We can find the answer as below.

Q: Describe the graph of the equation. r - 12cosri + 5sinsj -k O tis an ellipse in the z = -1 plane,…

A:

Q: Calculate the flux of the vector field through the given surface. F = zi + 2xj + 3yk, and S is the…

A:

Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i+5 sin(t)j+ 6tk;…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A:

Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

A:

Q: cos²(x) + 2cos²G) . cos³(x) - .dx

A: We have to find the integral.

Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

A:

Q: Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the…

A: As per our norms we have to write three multiple questions at a time kindly repost remaining…

Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Find curl (7z i + 8x j + 9y k). curl (7z i+ 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A:

Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y=…

A:

Q: Use the Newton-Raphson technique to find the value of a root of the equation e = sin 4x. An…

A: Given:

Q: Q2/ Check the symmetry of r² = -sin(20) %3D Ans./ Symmetry about the origin

A: Symmetry

Q: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

A:

Q: Suppose a product's revenue function is given by R(g) = - 2q? + 400g. Find an expression for the…

A: Given problem:- Suppose a product's revenue function is given by R(q) =- 2q2 + 400q   Find an…

Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

A:

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0,0). NOTE:…

A:

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

A:

Q: For the given function find dy/dx. = x + 2 %3D O y = 1-y-3x2-4x %3D 3y2 +2+2 O y = 1-a+3y-4x 322-y+2…

A: We know Implicit differentiation of ax+by=c is given by, a+bdydx=0 ddx(xn)=nxn-1 , for any real…

Q: 1

A:

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.004q - 0.9q + 615. The…

A:

Q: Evaluate the integral. V3/2 dr V1- r2 |

A: We know, ∫dx1-x2=sin-1(x)

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 y…

A:

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

A:

Q: For the straight line defined by the points (1,57) and (3, 87), determine the slope (m) and…

A: Solution is done in step 2

Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: 1+tan-1x D. y = + sec-1xcsc¯1x + xsin-1x +V1 - x2 2-3tan-1x

A:

Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

Q: 2. Solve the equation for 0 if 0<0 < 2n. Give your answer in degrees. 2 sin 0 – sin 20 = 0 %3D

A: Given problem:- Solve the equation for 0 if 0≤  θ  ≤ 2π ,Give your answer in degrees. 2sin(θ) - sin…

Q: Consider the points A(1, –3, 4), B(2, –5, 2), C(-1, –4, 2), and D(2,3, –5). (a) Find the volume of…

A: Let a,b,c and d are position vectors of point A,B,C and D resp. Therefore a=i-3j+4k b=2i-5j+2k,…

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: 1. Find all relative extrema and soddle points of the functon Use econd Partials Test where appli…

A:

Q: Solve

A:

Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

A:

Q: dx V2+Vx-1

A:

Q: Find the conservative vector field for the potential function by finding its gradient. g (x, y, 2) =…

A: We need to find conservative vector field.

Q: Use the first fundamental theorem of calculus to find F'(x) F(x) = [ cosr' dt

A: