Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y = −(ln9)x + 2. Leave your answer with exact values.

Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t,    y(0) =…

A: Given :y'' − y' = et cos ty(0)=0, y'(0)=0

Q: Find the extrema of the following function on the given interval, if they are any, and determine the…

A:

Q: Find the average rate of change of g(x) = 5x³ + 4 from x = - 4 to x = 4.

A:

Q: 7. y = (x+1)* 9. y = Inlog, x

A:

Q: -πl-π" ㅠㅠ Using the technique of substitution with u = • ITT -T, the terms of u as 1 -1 -1- du (a)…

A: This question can be solved using the concept of integration by substitution.

Q: (b) Given that s² + 16 (S-1)(s+3)(s²+4) Evaluate the values of A, B, C and D. A B Cs + D (s-1) (s+3)…

A:

Q: Solve the differential equation (24xy + 40y²) + (8x² + 40xy)y' = using the integrating factor µ(x,…

A:

Q: Compute the value of representation ³√√√3-i in exponential representation and polar

A: Given :3-i3

Q: Which of the following gives the area of the region bounded ㅠ by the curves y = sin x, y = sin(2x),…

A:

Q: PROBLEM/SITUATION: 1.) Prove that the product xy of two real numbers x and y is nonnegative if and…

A: We have to prove that product xy of two real numbers x and y is non-negative if and only if the…

Q: dx √(1-x²) 7. The value of f A. CONNE Oc O J. N is B. sin '(x) + c 4 C.rosx + le D. cosx A 8. Jcos'…

A: I am attaching image so that you understand each and every step.

Q: The graphs of the functions f(x) and g(x) are shown below. y 11 10 9 8 7 6 85 14 (a) Find (f. g)(2).…

A:

Q: b) Give the augmented matrix associated to the system of linear equations above. Answer: sin (a) ə…

A: The simple matrix

Q: 7. Given: [x,y,z]= [1,-1,5]++[3,4,7], determine the symmetric equations for the line If (13,15,23)…

A: Explained below

Q: six 3x sin B. Sin³ x + sinx+c Csix 3 x sinx D.six x + A B C

A: We will solve the problem

Q: Use the formula: PMT= (PV) 1-(1+i)*

A:

Q: d dx [47 tot 1 3x17 5 13 + 10 L 25 +100

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Find the derivative y = x tan^¹x − In √√1 + x²

A:

Q: Which of the following gives the area of the region enclosed by the line y = -x − 1 and the parabola…

A: The simple diagram then horizontal strip...

Q: Let S = { 1 - (-1)" | n € N}. Determine inf S and sup S. Justify. n

A: We have to find the infimum  and  supremum  of the given function.

Q: Which of the following gives the volume of the solid obtained by rotating the region bounded by y =…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: x TC Q2\ Find The Area under the curve Y= 4sine between X= and 2 X= π by the double integral method.…

A: Let's find area by using double integral method. Small mistake in given question, there should by…

Q: Consider the following differential equation. (x + 1) + (x + 2)y = 4xe-x dx Find the coefficient…

A: Transient term in a general solution of a differential equation are those terms that tends to 0 as x…

Q: 2 Σ(-1)+1n? + 5 m2 + 4 n=1

A:

Q: Solve the given differential equation by finding, in-imanapi 12xy dx + (4y + 18x²) dy = 0 Sectioner,…

A:

Q: Derive the Maclaurin and Taylor Series of the function below:

A:

Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: 5. Determine the area below f(x) = 10 - 2x² and above the line y = 3. 6. Determine the area bounded…

A: Given problem:- Determine the area below f(x) = 10 - 2x2 and above the line y = 3

Q: What is the sloe of the tangent line to the curve x = 3 sin y at the point (0, 2π)? 3. O O ا انت 3…

A: What is the slope of the tangent line to the curve x= 3siny at the point (0,2π) ?

Q: Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify…

A:

Q: Find all values of m so that the function yemx is a solution of the given differential equation.…

A:

Q: Question 3 (a) (b) Show that the solution y(t) of the initial value problem has the Laplace…

A: This question is all about laplace transform.  We know that laplace transforms are as  L{y"} =…

Q: Find the area of the surface generated by revolving the curve y = 2√x, 1 ≤ x ≤ 2, about the x-axis.…

A:

Q: 207 Σ=15 (11). Find sum Σ 15

A:

Q: ate the following integral using polar coordinates 17 'yx² (x² + y²j2dxdy

A: Above question is solved.

Q: Evaluate /1-(y-1)² by first changing it to polar coordinates. 219 dx dy

A:

Q: Q3. Use the integral test to determine whether the series, n=1 divergent. 1 (n+1)√n+1 is convergent…

A:

Q: derivative. (a) lim (b) lim Ax→0 In(e¹ + Ax) - 4 Ax In w w 1 w 1 =

A: Using L hospital rule

Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

A:

Q: 2. Line I has the equation y = 3x - 4. Line m has the equation y = 3x + 2. a. Graph each line on the…

A: Given line equation is in form of :               y=mx+c              where m= slope of line…

Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11.

A:

Q: Solve the following definite integral problems 1. Determine the area below f(x) = 8x - 2x² and above…

A:

Q: Which of the following is correct in solving 20 2x√2 + x dx? (a) Substitution technique can be used…

A:

Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11. 4. Determine the area to…

A:

Q: Given the piecewise function below, find the value of which makes the function continuous. -I f(x):…

A:

Q: d the absolute extrema if they exist, as well as all values of x where they occur, for the function…

A:

Q: Evaluate [ (cos² 0 + 2 csc² 0 + sin² 0) do .

A:

Q: Find an Integrating Factor, then solve the Non-Exact differential equation. (Non-anonymous question)…

A:

Q: Which of the following double integrals will NOT give the volume of the solid bounded above by z = 2…

A:

Q: Quadrilateral MATH is shown. LO 5- 4 -3- 2- M A -5-4-32-10 1 2 3 4 5 -1 T H -5- Quadrilateral MATH…

A: Given data :- M(-1,1) , A(1,1) ,T(2,-2) , H(-4,-3)  Dilation with scale factor of 2.5 Center of…