5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6 = 0

Q: 1. Siste dx It sex x

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: How many square units is the area enclosed by y + 2x - 5 = 0, y = 4x - x² and x² - 4y = 0 ?

A:

Q: x+3 x ³ + 8x² +16x S da

A: To evaluate the given integral by using partial fractions.∫x+3x3+8x2+16x dx

Q: 2 S-2 2 S+2 Option 3 Option 2 O *The Laplace transform of the x(t) is 2e21 1 S - 1 s²+1 Option 1 O…

A: Let's do laplace transform of given function.

Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

A: Here we have to choose the correct option.

Q: If you apply the limit comparison test to assess convergence 1 - to which of these series would you…

A:

Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

A:

Q: Find the derivative: y = ln (3x + 1) O y = O y = Oj = 2 y = = 2ln(3 + 1) (3x + 1) 6 (3x + 1) 3 (3æ +…

A:

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

A:

Q: TT/6 6² tan 2x dx =

A:

Q: Find the area common to the circle r = 3 and the cardioid r = = 3(1 - cos 0)

A: Figure of area enclosed by both curve÷

Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.

Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

A:

Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below:

Q: Find f(t). ℒ−1{(2s + 7) / (s2 + 8s + 65)}

A:

Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

A:

Q: 7- (a) If a is a constant and cannot be equal to 0, find the critical points of f(x) = 3a + 6x (b)…

A:

Q: solve the differential equation for initial value problem using the method of undetermined…

A:

Q: Its tot as TR = 300q - 6q² and its total costs as TC = 4q². a) Determine the optimal quantity and…

A: Given

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: Consider the following. f(x)={-2x - 4x + 3, x≤ 4 X > 4 Find the x-value at which f is not…

A:

Q: 1. f(x) = 4x - 17

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Let f(x)= Select the correct description of the one-sided limits of f at x = 0. Choose 1 answer: lim…

A: Above question is solved.

Q: 1- Calculate the area of the region which is bounded by: y = (x - 1)², y = (x-4)2, and y = 0.

A:

Q: if X(z) is the z-transform then what is the z-transform of x(n) of x(n- ?6)

A: In this question, we need to find the z transform of x(n-6).

Q: dx f(x2²x+10) ² २

A:

Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: Given problem:- A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup.…

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

A:

Q: ng expression:

A:

Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7)

A: The solutions are given below:

Q: Investigate if the integral dx 1-x is convergent or not. Justify your answer.

A: Divergent

Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

A:

Q: Write the first five terms of the sequence: {√n² + 2n = n}=1 Determine whether the sequence…

A:

Q: dx sin x tanx

A: Here we have to solve only part b

Q: Let f(x) be the function 5x² - 7x + 6. Then the quotient f(5+h)-f(5) h can be simplified to ah + b…

A:

Q: Find dy/dx for: y cosy = xy Y O -y sin y+cos y-x Y cos y-x Y -y sin y-x 1 cos y-x O O O

A: Given :y cosy= xy

Q: Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled…

A: We have to solve above problem.

Q: Instructions 1. Write your complete solution for each item. It should be handwritten. 2. Make sure…

A:

Q: Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y"…

A:

Q: 2 S² T ㅠ 1-cos x dx 2

A:

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

A:

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: Find dy dx In y = e sinx O dy dx O dy dx O dy dx O dy dx = yey sin x =yey cos x = 4 1- ye cos x yey…

A: We can find the answer as below.

Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

A:

Q: 2 z² +4 lim z 2i 2z²+(3-4i)z-6i

A:

Q: Consider a plate (the plate has the same shape as the region enclosed by y = x² and y = 4) submerged…

A: Let's find force(F).

Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: Find the integration of the following functions COSX 1) dx 3+8sinx 2) fx tan(x² + 1)dx

A: In this question, we want to solve the given integrals.