Use partial fraction decomposition to evaluate the integral: 6r - 3 1² - dr = 2-r-20 Be sure your variables match those in the question.

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: g. What is the range of f(x)?

A:

Q: Show that div curl F = 0 assuming that F is continuous and has continuous partial derivatives of…

A:

Q: 5. f(x) = x², 6. f(x) = 1- - g(x) = 4x + 5 3 x + 3 7. f(x) = x + ₁1/2x - 3, g(x) = 1 x-1 g(x) = 3

A: As per guidelines we can answer only one question at a time so if you need more answer kindly repost…

Q: Consider the function f(x)=√x and the point P(4, 2) on the graph f. (a) Graph fand the secant lines…

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Q: Solve for x, to two decimal places. 200 = 4(5)* O a) 10.00 Ob) 2.43 Oc) 12.15 d) 1.87

A: The given equation is: 200=45x   As we know from the logarithmic property, logbxa=a·logbx  where…

Q: Find the limits. f(x) = 2x²-3x + 15, g(x)=√√x + 3 3

A:

Q: 12/ A company is manufacturing two types of autocycles for gents and ladies separately, which are…

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: 1. A radioactive substance with an initial mass of 5kg has a half-life of 30 months. a) Write an…

A: Answer is in next step!

Q: (a) Find f(-21) and f(-6). f(-21) = f(-6)= (b) Find f(18) and f(0). f(18)= f(0) = (c) Is (6)…

A:

Q: (a) Evaluate the limit 9n²-n+9 lim n o 13n2+8n+15 Enter the exact value for your answer. 数字 (b)…

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

Q: You are also given a translation of the graph of y = |x + 11. -10-8-6-4-2 ⁹⁰ Write an equation for…

A:

Q: the directional derivative of f(x,y) = y^4+2xy^3+x^2y^2 at point (0,1) in the direction v = i +j is…

A:

Q: Twenty-four people enter a tennis tournament. How many different first-round matches are possible if…

A: Given , 24 people enter a tennis tournament, and each can play with any other player.  It means 1st…

Q: Complete the table to find the derivative of the function. Original Function 1 5x4 y = Rewrite X…

A:

Q: use the graph of the function to find the domain D and range R of f(x) and the indicated function…

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Q: Find an equation of the tangent line to the curve at the given point. y = 2ex + x, (0, 2) y 11

A:

Q: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it…

A: Topic-Linear function

Q: 3. Which of the following is a transformation applied to the base function ƒ(x) = 2(x + 3)² + 6 a) A…

A:

Q: What is the limit of f(x) = 7 as x approaches ? (If an answer

A:

Q: 4 Write as a single logarithm. log x² + log xª O a) log x6 b) log x8 c) log x²√√x d) ¹ log x8

A:

Q: Let f(x) = 2x = 2x − 3 and g(x) = x² + 3x + 4. Evaluate the following. a. f(3) = 3 b. f(-4)=-11 c.…

A: As parts a,b,c and d are already correctly marked, the solutions for remaining questions are given…

Q: 30° 19 The height of a right triangle with base angle 30° and base 19 is Q

A:

Q: 1. a) b) -16807 32 10 √√–128 -3

A:

Q: Suppose an object is fired verticall- upward from the ground with an initia velocity of 96ft/sec.…

A: Topic:- calculus

Q: The foci are on the x-axis, the x-intercepts are ±2 and they intercepts are ±1.

A: find the equation of ellipse

Q: Determine the exact value for cot the CAST rule. 11л 6 without using a calculator by using special…

A:

Q: help

A:

Q: At 1:00 P.M., a thermometer reading 70°F is taken outside where the air temperature is -10°F (ten…

A:

Q: simplified

A: Please refer to the image below

Q: Find the derivative of the function. f(x) = 4 3 VX + 2cos x

A: To find the derivative of given function

Q: X y 2 3 4 7 8 5 7 9 5. 10 11 X 12 y 3 14 5 6. 12 7 18 9 11 11

A: Here, the domain of the function is the set of input values, that are x, and the range is the set of…

Q: Determine whether the following vectors are: -1/√√3 1 1/√3 0 1/√√3 2/3 - 1/3 0 - 1/3 Orthogonal but…

A:

Q: If 2x³ — 9x² + 4x 7 is divided by x - 3 to give a quotient of 2x² – 3x 5 and a remainder of -22,…

A: We know Dividend=Divisor ×Quotient +Remainder

Q: 10. What is the amplitude of the function f(x) a. 12 b. 5 c. 4√10 = 3(sinx) + (4cosx)? d. 3√10

A:

Q: (b) The graph of y=h (x) is shown. Draw the graph of y=h (2x) −3. -8 -6 -4 -2 8- 6- 4 2- -24 -4 -6-…

A: The graph is given below

Q: Perform the following conversions. a) The line 5x + 7y - 35 = 0 to vector form. b) The plane [x, y,…

A:

Q: (7 − 2x)10 dx

A:

Q: Find the exact value of the following expression for the given value of 0. Do not use a calculator.…

A: The given expression is tanθ4 if θ=2π3 use the trigonometric ratio and values,…

Q: The angle of elevation to the top of a building in New York is 10° from the ground and 1.25 miles…

A: Given query is to find the height of the building.

Q: Convert 1 -Tradians to degrees: 2

A: convert 12π radians to degrees

Q: State the derivative. Do not simplify. f(x) = log(x) + log₂ (x)

A:

Q: y = C₁ cos(2x) + C₂sin(2x)

A: Given: Now,      y'=c1cos2x+c2sin2x' =-2c1sin2x+c2cos2x· 2y''=c1cos2x+c2sin2x'' =-4c1cos2x-4c2sin2x…

Q: (a) Show that the vector field F(x, y) = (x², y²) is conser- vative, then find the potential…

A:

Q: Find f ∘ g ∘ h. f(x) = √x − 3 g(x) = x2 h(x) = x3 + 1

A: Topic:- function

Q: Show that the surface area of a sphere with radius a equals 4ra². r(u, v)= (a sin u cos v, a sin u…

A:

Q: An arc of length 19 meters subtends a central angle of 294 in a circle. a) Find the circumference of…

A: Topic:- geometry

Q: 1. (a) f(-2) (cf (1) ๆ -3 (b) f(−1) (d) f(1.5) 3

A: The graph of the function is:

Q: Find the limit L. Then use the - definition to prove that the limit is L. lim √√x x →0 L = Use the -…

A: To find the given limit L. Then by using ε‐δ definition to prove that the limit is L.limx→0 x3

Q: (a) If A=[ay] is a 3x3 matrix; such that ay = i (4-²), find the values of diagonal elements and the…

A: