Use the substitution t = tanto transform the integrand into a rational function of t and then evaluate the integral. ¹(₹) · π/2 5 sin(2x) dx 2 + cos(x)

Q: Suppose f(x) = - = (x − 6) (x + 3). a. Solve (x - 6) (x + 3) = 0 for x. X = 6,-3 b. What are the…

A:

Q: Iflog, (2)=0.4752, log, (3)=0.7532, and log, (11)=1.6440, what is the value of the following…

A: If , then to find the value of .

Q: O 2x+8 4. Use the definition of the derivative to find (x+h)²+8(x+h)-4-x²-8x+4 h | f'(x) of f(x) =…

A: The objective of this question is to find the derivative of the function f(x) = x² + 8x - 4 using…

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A: the curve y=x3−x at the point (−1,0)here needs to find the equation of the tangent…

Q: Find the value of the determinant D given by: a 6 3 d -4 D = c 6 9 9 where a = 2, b = 5, c = 12, d =…

A: The given determinant is

Q: (a) Find a simplified form of the difference quotient and (b) complete the following table.…

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Q: 1. Consider the differential equation y" + 2xy" - z²y = x^sin r. (a) Is this a linear differential…

A: Note ::- According to our guidelines I answer the first one. Kindly repost the other question…

Q: F(x) = {e^ X-3 OLX Find lim F(x) x 70 im f(x) x 70

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Q: 13. Match each parent function with a characteristic of its graph. Each example may only be used for…

A: We see the given graphs and determine the from which of the given options is a better characteristic…

Q: 9 5. Find the equation of the tangent line to the curve y = x² + 3x - 1 at x = 2

A: Given,.Given at x=2.

Q: Suppose ƒ is a quadratic function that has roots at x = - 3 and x = 7, and f(0) = 15. We will write…

A: f(x) has roots at x=-3 and x=7 and f(0)=17

Q: Complete the square and find the minimum or maximum value of the quadratic function y = x² 18x + 88.…

A: Given Quadratic Equation is as follows

Q: 3. What product is shown by the model?

A:

Q: 22. lim √x + 6 x 3 x + 2

A: To find :-

Q: Differentiate the function. 4x²-7 y= 3 9x + 4

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Q: 2 2 t²-9 1 t²-2t-3

A: P(t)=2t2−9−1t2−2t−3

Q: Consider the bases v₁ = (1,0)¹, v₂ = (0, 1) and v₁ = (2, 1), v₂ = (1,3)¹ of R². The transition…

A: The objective of this question is to find the transition matrix that transforms the basis vectors…

Q: 2x² + 4x = 5

A: 2x2+4x=5

Q: 22. 1 + √2,1 - √2, and 3

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Q: Consider the function g given by g(x) = |x-2| +5. (a) For what x-value(s) is the function not…

A: Differentiability

Q: Assume that the function f is a one-to-o (a) If ƒ(4) = 4, find f¯¹(4). Your answer is (b) If ƒ−¹(−9)…

A:

Q: limh→0 -2 0 √2+h-√√2 h 2 represents the derivative of f(x) = √ at x = a. What is a? a cannot be…

A: Given,Given derivative of f(x) at x=a is,

Q: 3. Find the total area between the region and the x-axis. a. y = -x² - 2x, -3 ≤ x ≤ 2 b. y = 3x² -3,…

A: To find the total area between the region and the x-axis.

Q: A rock is thrown upward from a bridge that is 96 feet above a road. The rock reaches its maximum…

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Q: The expression below has been simplified on the right hand side. What are the correct integer values…

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Q: matrix A given by: a11 a12 a21 a22 a31 a32 A where: A = BC and: B = and C = 1 2 4 C 7 8 a d e a13…

A: Need to find out  the product of  the matrices

Q: Refer to the graph of y = f(x) to the right to describe the behavior of lim f(x). Use -∞o and co X-3…

A: Refer to the graph of  below to describe the behavior of .

Q: 23. (1) the domain of f is (-∞0, 0] (ii) f(-2) = f(0) = 1 (iii) lim f(x) = +∞ --x

A: The given conditionsThe domain of f is (-]

Q: technology for x1, x2, x3, x4, and z. If there is an infinite number of solutions then express the…

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Q: 3. Find the set of all points (x, y, z) that are twice as far from (3, 2,0) as from (3,2, 6).

A: Suppose the set has a point   Plug into the distance formula:   and   is and   is

Q: ist the x-values in the graph at which the function is not differentiable. -3 -2 -1 Ay 3+ 2- 1- 14…

A: Here we will use the concept  curve of the graph

Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: L₁: L₂: Xo = Yo = Zo || x=6+1, y…

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

Q: Find f'(a). f(t) = t³ - 5t

A: Given,

Q: Simplify cot (t) csc(t)- sin(t) sec (21) + 1/2013 tan(2t) to a single trig function with no…

A: Cot(t)/[csc(t)-sin(t)]

Q: The Intermediate Value Theorem can be used to prove that the equation x² +7x+10=0 has at least one…

A: The objective of this question is to determine whether the Intermediate Value Theorem can be used to…

Q: Find the indefinite integral. √1+3t dr Select one: O a. (31-2)√3t+1 9 O C. O b. 2(3-2)√√3t+1 +C 27…

A: Given Integral is as follows

Q: If y= 8 find y' (4).

A: Given that the expression

Q: 21-26 Sketch a possible graph for a function f with the speci- fied properties. (Many different…

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Q: The slope of the tangent line to f(x) = 3x² - 1 at x = 2 is 12. true false

A: The objective of the question is to verify if the slope of the tangent line to the function f(x) =…

Q: Determine whether the line and plane intersect; if so, find the coordinates of the intersection. (a)…

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Q: Please help step by step

A: The objective of this question is to solve the given equation for the variable x.

Q: Find the distance between the parallel planes - 2x+y+z= 0 and 6x - 3y - 3z — 13 = 0. NOTE: Enter the…

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Q: Determine the wronskian of the given set of functions and determine whether they are linearly…

A: given

Q: First find f' and then find f. f" (x) = 2x³ + 10x² + 6x +1, ƒ'(1) = 4, f(1) =-10.

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Q: Find the exact solution(s) to the following equation. log(x+2)+log(x-2)=3

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Q: Determine whether the given function is continuous. You can verify your conclusions by graphing the…

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Q: Pls help ASAP

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…