SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER UNDERSTANDING. 1. [csc(5x - 2) + cot(5x - 2)]³dx

Q: Evaluate the following limits algebraically. 2. lim x---> 2^-      (x+4) / (x^2 + 2x - 8) 4. lim…

A: To evaluate the following limits.

Q: Let y = f (x) be the particular solution to the differential equation with the given initial dy dx…

A: The given initial condition is .The aim is to find the tangent line to approximate to .

Q: (5) Are there other shapes that would hold the same volume yet have even less surface area? Let's…

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Q: Express your answer as a polynomial in standard form. f(x) = 2x² 5x – 12 - g(x) -2x + 2 = Find:…

A: f(x)=2x2-5x-12g(x)=-2x+2

Q: Evaluate S 2x + 1 (4x + 3)(x + 1) - dx

A: Consider the integral

Q: Find the intervals on which the graph off is concave upward, the intervals on which the graph off is…

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Q: Find an antiderivative of the function g(x) = 6x³ +7. An antiderivative is

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Q: Use trigonometric identities to solve the equation in the interval [0, 2). 2 cos ²0-sin 0-1=0

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Q: Find the value of (f o g)' at the given value of x. Assume that f'(3) = 6, g'(4) = -5, g(4) = 3, and…

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Q: 1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke…

A: Here given a different sentences.The objective is to check that the given sentences are valid,…

Q: Consider the parametric curve: x Y 4 +² +³4t At which t value(s) is the tangent to this curve…

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Q: 37. se sec² (10x + 7) dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: A biologist has two brine solutions, one containing 2% salt and another containing 8% salt. How many…

A: The objective of this question is to find out the amount of each brine solution needed to create a…

Q: Find the exact value of the integral using formulas from geometry. (3 (3+x)dx a) Write which…

A: We have to find the exact value of integral using formula from geometry.Given integral Here…

Q: lim       sin(π+h)- sinπ                                      h→0     —------------…

A: Note:-Since your part a incomplete ,please repost part a again(b)

Q: Let f(x) = 3x - 6 and g(x)=x+3. Find each composite function and describe the domain of the…

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Q: Find the radius R of convergence for the series R = n=1 n! xn nº

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Q: g. y = tan x h. y = t+√√2t+√1-5t

A: To find the derivative of the following functions.

Q: 2 sin(x) cos(x) + √3 sin(x) = 0 Find all angles in radians that satisfy the equation. For each…

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Q: Find the area of the region enclosed by the curves between their intersections. y=x² and y= 2x

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Q: Find the area of the region between the curve and the x-axis. f(x) = 16-x², from - 7 to 7

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Q: Determine whether the function shown below is a one-to-one function. If it is one-to-one, find its…

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Q: Please do part a)

A: The objective of this question is to find the general solution of the given linear nonhomogeneous…

Q: 15 x² 3x 54 (Round the answer to four decimal places.) Find the area bounded by y = X- -, x = 3, x4,…

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Q: Evaluate the following: lim In(e+h)-in e

A: To evaluate the following limit.

Q: 11. Use the graph of f to sketch the graph of f'.

A: The given graph of f

Q: 7. Determine where fis discontinuous. Justify your answers. √=x if x < 0 3-x if 0<x<3 (3-x)² if x ≥…

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Q: Write the integral required to find the area of the region pictured below that is bounde 2(y+2) 3…

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Q: (– ²/6) has exactly one point of inflection with a positive x-coordinate. What is the x-coordinate…

A: The given function is .The aim is to find the point of inflection.Definition:If  is an inflection…

Q: A 17 ft. ladder is leaning against a building. The foot of the ladder is currently 9 ft. from the…

A: We have to use the concept of derivatives

Q: Find the center, foci, and vertices of the ellipse. Graph the equation. 4(x + 5)2 +8(y-2)² = 32 Find…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: The objective of this question is to find the critical numbers of the given function f(x) = 12x -…

Q: 2 Assume that f'(2) = -9, g'(3) = g(3)=2, and y=f(g(x)). What is y' at x = 3?

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Q: (b) Use Desmos to graph the surface area function on the following coordinate system. Label each…

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Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: Let sinA=-4/5 with A in QIII and cosB=-3/5 with B in QII. Anwer Exactly. Find sin(A-B), cos(A-B),…

A: Given,

Q: 6. Find the equation of the line tangent to the following functions ate the given points. a. y = x²…

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Q: Convert the following equation to polar coordinates. x=2y² The polar form of x = 2v² is. (Type an…

A: Given,

Q: Find the general solution for the following linear homogeneous recurrence relations: (a) an = 2an-1…

A: The objective of the question is to find the general solution for the given linear homogeneous…

Q: Let A and B be the following matrices. Perform the following operations: -6A A+ 3B: 2A + 4B A 9. 5…

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Q: Vs = ft - f- f+ + f =

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Q: Find the limit as a number, ∞o, or -∞o. Otherwise enter DNE. lim [√(√An+1 = √an)] = [ 4n n→ ∞o

A: Limn-infinity [sqrt(n) (sqrt(4n+1)-sqrt(4n))]

Q: 3 · [²³ F(x) Given 6 ³ fº f(x) f(x) dx = 9 and Exercise (a) 6 [° F(x) f(x) dx = -8, evaluate the…

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Q: x3 x² + 4x +3 Example: ₁ dx

A: We have to perform the partial fractions

Q: Four Calculus II students have solved I sin sin(x) cos(x) dx. Their solutions are below. Use what…

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Q: Find the arc length of the graph of (y − 1)3 = x2 on the interval [0, 8]

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Q: Find the area of the region between the curve and the x-axis. 2 f(x)= x(x² -26), from - 5 to 5.

A: The region is bounded by curve  and x-axis from

Q: Let g(x) = f(t)dt, where f is the function whose graph is shown. y f 20 (a) Evaluate g(0), g(4),…

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Q: Question Find the area A of the region that is bounded between the curve f(x) = -2 sin () - 3 and…

A: To find the area A of the region that is bounded between the curve  over the interval .