3. (a) Calculate sinh (log(5) – log(4)) exactly, i.e. without using a calculator. Answer:

Q: Consider the following initial-value problem. 4 f'(x) f(9) = 31 %3D Integrate the function f'(x).…

A: We have to find the function.

Q: 16. If r'(t) is the rate at which a water tank is filled, in liters per minute, what does the…

A: topic- derivative and integral

Q: x dx dy _dy V4 +

A:

Q: Evaluate: sin 6x sin 3a da A. 0 в. - В. 2 C. - :- С. 2 D.

A: SOLUTION-

Q: dx 4 sın*3x tan

A:

Q: 2х + 1 (х — 2)(х — 3)2

A:

Q: In x2 lim

A:

Q: In ly-y-cf dy

A:

Q: Suppose f(x) is a function that satisfies the following inequality for all x: 1+3 cos(x) < f(x) <…

A: Solution: The given inequality is

Q: ind the maximum product of two positive numbers given that the sum of the umber and twice the second…

A: Please refer to the image below

Q: Change the following rec 15. x = 6y + 8 %3D

A: The given equation is x+6y=8.

Q: Find the common elrea between Y=2CI+Cose) and carved V=Z(1-Sine) which is Losatel in the funrth…

A: Let's find common area between given two curves. Common area in fourth quadrant.

Q: x2 — х +1 dxp х2 + 2х + 2 x2.

A: Topic:- application of integration

Q: 3. Find the reference angle (also called the reference number) for the angle: 13n radians. 11

A:

Q: Supply the missing integrand and limits of integration. dy (3x² – 2xy + y³) dx dy

A:

Q: dy If y=u? and u = x3 + 4 determine dx

A:

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hopital's Rule. sin(9x) lim 7x…

A: We have to find the limit

Q: Which of the following angle measure is coterminal with an angle whose measure is 798°? -78° -278°…

A: Let the angle be theta.

Q: sec x lim X0 n x

A: Here we have to find the limit.

Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use co or -, enter INFINITY…

A:

Q: Evaluate the given integrals. 1. ſ cos v2x dx 2. fx a*dx

A: Please see the answer below.

Q: (hen? + h? eh* ) di

A: The integration of the integral is  (heh^2+h2eh^3).

Q: Write an equation for the polynomial graphed below 5+ 4 2+ 1+ -5 -4/-3 -2 -1 -1 1 2/34 5 -2 + -3 -5+…

A:

Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

A:

Q: 9. State whether each of the following functions is convex, concave, or neither. (a) fo -e (b) f) -e…

A: Note- as per our guidelines we have to answer only first three parts if multiple parts are posted in…

Q: Two particles have positions at time t given by S1= 4t - t2 and s2 = 5t2 - t3. At the instant the…

A:

Q: 19. For the following function f (x) 3x-4 %3D find any x-intercepts, y-intercepts, and equations of…

A:

Q: A city had a population of 2,238 at the begining of 1965 and has been growing at 9.6% per year since…

A: TOPIC- EXPONENTIAL FUNCTION

Q: -6(х— sin "x)(csCx «)(cs 3 CSC X |

A: Topic:- function and trigonometry

Q: Find the enclosed area by the curve with equation f (x) = x² – 4 and g (x) = 8 – 2x2 40 35 36 32

A: To find the enclosed area between given two curves.

Q: Solve fo x: 3csc(x) + 2=0

A:

Q: Which of the following statements involving sigma notation is always true? η η η Α) E (ak bR) = E…

A:

Q: Supply the missing integrand and the limits of integration - 2sin 0 r cos?0 dr d0 = _d®

A:

Q: 7. Evaluate the following. 2 erty? + 29)dy dz A. 30 5.4 B. C. 2.3 D. 4.9

A:

Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

A:

Q: Evaluate the limit, using L'Hopital's Rule if necessary. In x lim

A:

Q: Find the particular solution of the differentlal equation that satisfles the Initlal condition(s).…

A: First integrate and satisfied given condition

Q: A woman 1.5 m tall walks directly away from a street light which is 6 m above the ground at a rate…

A:

Q: D. Define the multiplication operation * as modulo 10 in G = {1, 3, 5, 7,}. Cr table for this.…

A: Topic:- algebra

Q: Consider the following initial-value problem. f'(x) = 6x2 – 8x, f(3) = 21 Integrate the function…

A: Given: f'x=6x2-8x, f3=21   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: (ax-2) dx x2+ 2X + 15

A:

Q: Given the vectors v and ü, answ v= 10i + 2j - 11k u=7i+24j a. Find the dot product of v and u. Find…

A: calculation of above requirement are as follows

Q: 1. Determine whether the series En=1 2n4+1 is convergent and explain why.

A: We have to find the convergent As per guideline we have to solve one question Please repost other…

Q: Solution: Here * = Sin x The graph is Ine Shadded negion find i The required of we have to the area…

A: Let's find  area of given curves y=e^x from x=0 to x=1.

Q: 8. The general solution of y" + 4y = 3 sin 2x

A:

Q: IV. Suppose z is a function of r and y, and tan Vy² + x² = z*e®y. Solve for dz dz and

A:

Q: Find the area between the graphs of y = x and y = (x – 2)- | O 9/2 O 4 O -9/2 O 1

A: Given: y=x and y=x-22 Now find the point of intersection between the given curve and line. y=x ;…

Q: x*- 2x³+x² xdx

A: ∫x4-2x3+x2xdx ∫x2x2-2x+1dx ∫x2(x-1)2dx ∫x2(x-1)dx ∫ x3 -x2dx x4/4 -x3/3 +c

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A:

Q: g³ + x² + 2x+1 d.x (x² + 1)(x² + 2)

A: Explanation of the answer is as follows