Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x + sinh 3x)3 ... (cosh 3x + sinh 3x)3 =

Q: lim (fx) f(c) lim f(x) DNE X-4 f(4) = 3 Once again we see that lim (fx)) and f(c) are not the same. ...

A: Here, the given function is: f(x)=x3-1  

Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms, fractio...

A: Here we have to find the solution of given differential equation. 

Q: 2, 1³ – 6, if a 2 9. Determine whether each of the given limits exists or does not exist. a. lim f(x...

A:

Q: 4. The function f is defined for all real numbers. What is a reasonable estimate for lim f(x)? a. -5...

A:

Q: Solve the differential equation. dy 10x 16 - y, -4<y<4 dx %3D - The solution is (Type an equation.)

A: Topic = Differential equation

Q: Let r(t) = -6t2 î+ (t² +3) ĵ + 7 k for t > 1. Reparameterize in terms of the arc-length parameter.

A:

Q: 8) Which of the following functions are solutions of the differential equation y" + y = sin x? a) y ...

A: The given differential equation y''+y=sin x

Q: dx 3 -1 (4-x²)7

A:

Q: Find (f)(a). (x) = 3x + 3x² + 7x + 7,

A: We are given the following. We know that . So,         f-1'(7)=1f'f-1(7).

Q: Evaluate the following. Show solution using the basic formulas. 1. S(3x² – 8x + 7)dx

A: Let I=∫ 3x2-8x+7dxApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdxI=∫ 3x2dx-∫ 8xdx+∫ 7dxTake the constant o...

Q: Evaluate [z tn"(1 + x®)dx (1+x³) x². p 1 In³(1+x³) + C 1 In*(1+x³)+ C Option 1 Option 2 12 in*(1 + x...

A: topic - indefinite integral

Q: 1. Evaluate lim (2x-5) given its graph below. X-2 b. -1 c. 2 d. 1 а. О 2. Given the graph of f(x) be...

A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. (1+ cos x)y = sin x(sin x + sin x cos x- y)

A: Find your answer below 

Q: 1. Use the function f (x) = x² – 3 to answer the following questions" A. Find the average rate of ch...

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 7 V 1- sin(x) dx

A: Evaluating the indefinite integral

Q: 1. Using the table of values, estimate lim 3x x-2 а. 3 b. 6 с. 2 d. 5 2. Using the table of values, ...

A:

Q: 4. (x+ 2y-1)dx-(2x+y-5) dy =o

A: According to question,Given differential equation,x+2y-1dx-2x+y-5dy = 0

Q: . Find the domain of the inverse of the function f(x) = −3√4− x  + 5.

A:

Q: 5. Ydx - xdy + x(2 – y)dy = y? e dy

A:

Q: Direction: Find the derivative of the function. g(z) = (3 – 2") (zª - z + 1) Select one: g'(x) = -bx...

A: Given that: g(x)=(3-x2)(x3-x+1)

Q: ) Determine the volume of solid obtained by rotating the region bounded by y = x^2 – 2x and y = x ab...

A: 21) Determine the volume of solid obtained by rotating the region bounded by y = x^2 – 2x and y = x ...

Q: Let f(x) be a function and let a be a real number. Determine if the statement is always “True”; othe...

A:

Q: 2. For each of the following statements, determine if they are true or false. In either situation, e...

A: Find your answer below 

Q: A particle is moving along the graph of 7(t) = te-tî+ t² î+ 2t k. Set up the definite integral that ...

A: Here, the given curve is: r⇀(t)=te-ti+t2j+2t k

Q: Consider the function below. Use it to find the following limits. ² – 49 F (x) |r – 7|

A: Given that: F(x)=x2-49|x-7|

Q: b) f(x) = -log2(2x + 3) – 3

A:

Q: Combination 1. A panel of judges is to consist of four women and three men. A list of potential judg...

A: This question can be solved using the concept of selecting r objects from n given objects when the o...

Q: Find (fo g)(x) and (g o f)(x) and the domain of each. f(x) = x? - 3, g(x) = 4x – 5 (fo g)(x) = (Simp...

A:

Q: Evaluate: 1- cos(x) 3x2 lim Express your answer in 4 decimal places.

A: According to question,Given limit,limx→0 1- cos x3x2

Q: 1. lim f(x) = -1 and f(1)DNE %3D

A: In this question , we make a graph. when x tends to '1' , f(x) tends to -1. and f(1) does not exists...

Q: 2. Water is flowing in a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such...

A: Q=20 m3sg=9.81 ms2A=3y + y22B=3+yy= critical depthfy=1-Q2gA3BAim: We need to find theapproximate val...

Q: determine the value of k which will make h' (π/4)=6 when h(x)=In(cosx)+kx. a. 6 b. 5 c. 0 d. 7

A: Given, hx=lncosx+kx We have to find the value of k for which h'π4=6  

Q: x3-27 dx 2. ズ-3

A:

Q: P1. For each of the following infinite series: a) Determine n-th partial sum Sn b) Show whether the ...

A:

Q: |S(1 – cos 4u) du

A:

Q: Given the equation below. Give what is being asked. 3 3 sin -xcos, xdx a sin ucos udu 8 xpx, Find: a...

A: According to question,Given definite integral,∫04π3 sin638x cos638x dx = αβ∫0γδπ sin6u cos6u du

Q: Find the area of the sector of the circle. r= 28.35 ft, 0=24.401° O A. 345.28 ft2 O B. 171.14 f? O C...

A: We can find the area of the sector as below.

Q: - 2 lim,→8- х — 8 X

A:

Q: Evaluate the integral: x ln x dx Choose the most appropriate answer. 승nz- +C ,6 -In x 6 36 x° (ln x)...

A: We have to evaluate the integral ∫x5 ln x dx

Q: Solve the following DE using separation of variables or method used in solving exact DE

A:

Q: 5. This is the graph of the function f. The dashed lines represent the asymptotes. Select the x-valu...

A:

Q: 4 y = (x +3) Lax-1)

A:   Since you have posted multiple question as per guidelines we can solve only one question at a time...

Q: (1) хdy — ydx — Vx? + у? dx (2) — Зу? — у? sin x dx (3) (x2 + 1)4 — у2 + 1 dy dx

A:

Q: Given f(x,y) = x-y-3xy³. Evaluate fdx O 14y-27y3 +C 6 O -6y³ + 8y/3+ C O 6x2 – 45x + C 4 O 2x2 – 12x...

A:

Q: Find the integral of 12sin xcosxdx if the lower limit is 0 and the upper limit is 90°. OA 11.5 O B. ...

A:

Q: dt x-5

A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS. y'(2y - x e*Y) = 2 +yey

A:

Q: 16 13. Find an equation in Cartesian coordinates for the conic from with equation r = Identify the t...

A: Given that: r=165+3cosθ

Q: Solve the given differential equation by undetermined coefficients. y" + 4y = 5 sin 2x y(x) =

A:

Q: Sketch the graph of a possible function that illustrates the combination

A: