V. Determine the equation of the tangent line to the graph of g at the point where r = 1 if g(x)= In x – 4 tan-(2?).

Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y"…

A:

Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: The Partial Derivatives for the following: the function below f(x, y) = 2x² – 3y – 4

A: Here is the solution:

Q: Express the following sums using sigma notation. a. 7 + 8 + 9 + 10 + 11 b. 8 + 16 + 24 + 32 + 40 +…

A:

Q: potter forms a piece of clay into a cylinder. As she rolls it, the length, L, of the cylinder…

A: Given problem:- A potter forms a piece of clay into a cylinder. As she rolls it, the length, L, of…

Q: Find the slope of the tangent line to the curve la? + 4xy – ly = 11 at the point (2, 1).

A:

Q: Eliminate the arbitrary constants on the given equation: y = Ae + Bxe" O y = y' – 2y O y' + 2y +y =…

A:

Q: Compute the following limits: cos (x) (i) lim x3 tan(3x) (ii) lim

A:

Q: dy 18. 0 do 2y = 0 sec 0 tan 0, 0 > 0, y(7/3) = 2

A: Given problem:- θ dy/dθ -2y=θ3 sec(θ) tan(θ) , θ>0, y(π/3) =2

Q: lim x? O1 -25 25 -1 ||

A: The detailed solution is given below Thank you

Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

A: We have to find the limit of a function and find the expansion of 1/x

Q: dy for the function e²* = /2 sin (x + y)at the point 0, dx 6. Find 4

A:

Q: Choose the correct graph for y = cos x with the domain indicated: y= cos x, -2Asx<

A: Given, y= cos x -2pi&lt;=x=0

Q: 20 The slope of the function ƒ(x) = 5x - 5 is ______. 1 -5 5 -1

A:

Q: 12' >(- 1)"-'b. where b = n' 1=1 (n+2) 14"+3 a) Find and simplify bn+1 "q b) Test the given series…

A:

Q: The integral of the given function xVx + 1 dx is equal to a. 116/5 b. 116/10 c. 116/15 d. 116/20 e.…

A:

Q: A. Evaluate the following integrals. 1. S(Vcosx + sin x)*dx 2. S cos³ 3x dx 3. S tans 2x dx

A:

Q: Given the vectors v and u, answer a. through d. below. v= 6i + 2j- 3k u = 3i + 4j a. Find the dot…

A: We can find the dot product as below.

Q: Express the vector 7i - 6j + 6k as a product of its length and direction. 7i - 6j + 6k =[Oi+…

A:

Q: Q2. Do as required: (40 Marks) 1. Evaluate: f(x) = S, di at a = 1 2. Find the Taylor series of f…

A:

Q: the folium (meaning "leaf"). Descartes's scientific colleague Gilles de Roberval called it the…

A: Find your answer below

Q: a) [. :l: Determine whether the following series (-1)"5"-1n . 42n+1 n=1 is convergent or divergent.…

A: As per policy only first question is answered. Please refer to the image below

Q: S dx 2x-1 1. Vx+2

A:

Q: (x- 2)² , (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A:

Q: Problem #6: Find the equation of the line tangent to f(x)= cos² x- sin? 1 at x = -. - 5x 6.

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: A graph of y = f (x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: Graph of the function is given, we have to find its derivative graph

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

A:

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: The given function is: f(x)=x5+4x3+x, a=4f(4)=45+4(43)+4=1284f'(x)=5x4+12x2+1,…

Q: Use Newton's method to approximate a root of the equation 3x' + 3x* + 2 = 0 as follows. Let r1 = 2…

A:

Q: Evaluate the integral of tan 2x dx tan 2x- tan 2x +x +c tan 2x - tan 2x + x + c C. tan 2x --tan 2x…

A: As per guidelines, I can answer only one question. Since you have asked for multiple, so I did first…

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos² (a) COS sin (a)

A:

Q: 3. V4- (x – 3)²dx.

A:

Q: 75° 4 A = (b) 0.4 rad 15

A: Given, theta= 75° Radius(r)= 4 units We know that, Area of sector= (theta/360°)×(pi×r²) Substituting…

Q: 1- sin r 6. Find lim 1/2 CSC x Csc x

A:

Q: If the derivative dx (instead of .) exists at a point and dx = 0, then the tangent line at that…

A:

Q: Differential Equation Classify the following differential equations.  - DEPENDENT VARIABLE -…

A: We have to classify the given differential equations.

Q: 7 7 = 3, f(x)dx = 8, and g(x)dx = 5. Evaluate the following integrals. Sowar=s. 2 2 2 Sawak = -5 7…

A:

Q: 2t dt 8. (1²+2)°

A:

Q: The series 7 n3+ 9 n=1 6 n+ 1 is divergent. Select one: O True O False

A: Given query is to find that statement is true or false.

Q: 5. y = cot cot (sinx) 6. y = 5 sec sec (2x) + 20

A: We can solve question no 5 and 6 using chain rule as below.

Q: Write the sequence in closed form. Make sure to indicate the domain. 3 %3D aj = 5

A:

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

A:

Q: (d) g(x) = v4 – x²;(-2,2) 2 (e) f(x) = (x + 1)3; [-2,1]

A:

Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A:

Q: Maximizing construction costs The management of the UNICO department store has decided to enclose an…

A: answer is in next step

Q: a) [ Explain why the following series * (-1)" 00 Σ 1 + n5/2 n=1 is Alternating. b) ! : Use the…

A: Solve the following

Q: Question 19 Evaluate the integral given. c(2x)tan(2a)dx +C %3D > Next Question

A: To find out the integration.

Q: x = y+ Vz? – y² O y = x cos(ln|æ|+ C) O y = = sin(ln|æ| + C) sin -In|피 3 C cos-" (2) – In|æ| =C

A:

Q: Give an example of a differential equation  and  classify according to   order, degree ,linearity…

A: