2) a> Determine the value(s) of k such tPhat g'u)= 5if g Cc) (x) x2-2 b) Write the equation of the tangent to glx) when x=2 Write your answer in the form y- mx + b. Find the equation of tHhe tangent and the normal. the follo wing curve uhen x- 4

Q: Ql Find Ax

A:

Q: x = 2y X=y-8 -12 12 -8-

A:

Q: Write Tif the statement is true, or F if it is false. Write your answers on the blanks. dx x +C 3 2.…

A: 1.∫5x233dx=∫53x23dx=53x5353+c=x53+c1. T2.∫-45x544dx=-45x944×49+c=-5x94+c2. T

Q: 58. Particle Motion The position of a particle as it moves along a line is given by s(t) = – 12r +…

A: Given,           The position of a particle as it moves along a line is given by…

Q: Describe the surface. x² + z? = 7 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

A: The given surface is: x2+z2=7

Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

A:

Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

Q: dy Find given x' +y =8y. dx

A: Given  x3 + y3 = 8xy

Q: If 54 = the determinant of the matrix below. 3 -4 What is the value of x?

A: We can solve this as follows:

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: Surface Area All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is…

A:

Q: Using implicit differentiation, find the slope of the tangent line at the point (9,16) on the curve…

A:

Q: Q3 Find y ン ニ月(^)→ t(メッ) tanx 2 y-(1+x)

A:

Q: 1. S cot 2v dv 2. S tan*- dr 2 3. S (tan tan 5w +cot cot 5w )² dw sec (Inln x* ) dx 4. S 5. S Csc4…

A:

Q: Evaluate the definite integral. NOTE: Enter the ecact answer. 13 ti+t°j dt

A:

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j+tk; t= NG) - ||

A:

Q: The volume enclosed by the cylinders z= 5-x,z= 4x and the planes y = 0, x+ y =1. Solution

A: First we will draw the region and find limits for x, y and z

Q: Find the minimum point for the function f(x) = 5x – 14x2 – 11x + 1

A:

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: Here we will find the smaller and larger distance values,

Q: Give the parametric equation of the line that passes through the point (−4, 3, −5) and is…

A:

Q: Solve the following Initial Value Problem: y"+ 16y 0, x)= 2 and y'() = 5. %3D

A: Topic = Differential equation

Q: 1 dx x[9+(ln 3x)" 8.

A: use simple integration method.

Q: Su Find D. andR X -1 %3D Xマ→!

A: Explanation of the answer is as follows

Q: * Example: Find a harmonic Conjugate fer U= = X_ x+y2

A:

Q: dy Given 4x -9y =1. Find by implicit differentiation. dx

A:

Q: 1 In solving the antiderivative of f(x) = 2 - sin(x) by miscellaneous substitution, the substitution…

A: Here we have to use the subsitution.

Q: .2 dx I (w² – 25)5/2

A:

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A:

Q: x +x-6 F(x)%3D at x= - x+3

A:

Q: Set up, but do not evaluate, an integral for the surface area of the surface generated when the…

A: writing given function as x in terms of y

Q: dx :Ja-4)(x-1) Evaluate: 1 A (x-1) + C X- 4 B None of the given choices x- 4 + C х-1, © 3ln

A:

Q: A particular solution of the differential equation y+4y =8sin2x is Select the correct answer. O a.yp…

A:

Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

A:

Q: : Se' com (7e')cos (4e")de Evaluate: (A) -cos (3e") –cos (11e*) +C 22 -cos (3e*) + -cos (11e*) +C B…

A:

Q: Find the gradient of the function: y = (5x ln (x)/ 6) + x/3 at the point with x-coordinate 1. Give…

A: We can solve this problem as follows:

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

A:

Q: 2x + 1 -dx (Зх -1) (г2 + 2х + 2) Evaluate: F (x) = 2 In (|3.x – 1|) – In (æ² + 2x + 2) - 4 arctan (x…

A: A detailed solution is given below

Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

A:

Q: 25 – x² In -dx , if we let u=/25- x2 , then udu= – xdx. T True F False

A: Follow next step

Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: Q2 Find the limits 1- lim h +h cosh thcosh Sinh.cosh J4ズ メラ 2x-8

A:

Q: Q38: If y = e2x sin 5x, then which of the following is true? (a) y" – 4y' + 30y = 0 (b) y" – 4y' +…

A: Given,            y=e2xsin5x

Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

A:

Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: 8:44 C ing e Determine whether the series is convergent or divergent. 00 1 n = 1 The series is a…

A:

Q: S tan? 3y sec® 3y dy 2 tan 3y + tan 3y + tan" 3y + C O A none of the choices 2 tan 3y + 1 tan" 3y +…

A:

Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

A:

Q: Question 8 = 1 and lim,→a g(x) |8(x) If limx→a ƒ(X) = 0 then, we must have limx→a [f»]«® = 1 True…

A: We are authorized to answer one question at a time ,since you have not mentioned which question you…

Q: Select as many answers as possible. * Find the absolute extrema of the function 2/3 f(x)=(x+1)* in…

A: f(x)=(x+1)(2/3)    ,    [-2,1] f'(x)=2/3(x+1)(-1/3) At critical points f'(x)=0 2/3(x+1)(-1/3) =0…