State the trigonometric substitution you would use to find the indefinite integral. Do not integrate. (a) (25 (25 + x²)-6 x(0) = dx

Q: Which of the following integrals are improper integrals? answer(s). a) sin(3x) dx b) S (x-2)² c)…

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Q: compute r' (t)= and / r(t) dt= with C a constant vector. i+ i+ j+ j+ k k+ C

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Q: Evaluate the integral I. I = I = = [( (e¹i + 3t²j + ln (5t) k) dt i + j+ k + C

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Q: 2 2 use the graph to find the limits lim f(t) to

A: We have given that the graph, so find the limit using the graph:

Q: Determine if the series converges or diverges.

A: The series​​ converges.  Explanation:To determine if the series converges or diverges, we can use…

Q: a. f f(x)dx fo g(x)dx b. f f (x) dx * g(x)dx

A: We have to prove that part (a) and part (b) are not equal.Given f(x) = 4 and g(x) = 3.

Q: 1+x² What is the slope of the tangent to the curve y=- 2x when x = 3?

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Q: Suppose a sequence satisfies the recurrence relation and initial conditions given below. Find an…

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Q: For the equation given below, evaluate y' at the point (1, -2). e + 15 e 2 = 3x² + 3y².

A: ey+15−e−2=3x2+3y2

Q: c. Let h(x) = 0.75 sin(0.9x). i. What is the period of h? ii. What is the amplitude of h? Preview

A: h(x)=0.75 sin (0.9x)

Q: 3) What does the matrix 1 0 0 0 1 0 001 represent?

A: The matrix represents the identity matrix of size 3x3.Explanation:In the given, the matrix…

Q: MNPQ is a parallelogram and R is the intersection point of the diagonals MP and NQ. Let = MQ and =…

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Q: Compute f(g(x)), where f(x) = x and g(x) = 8x - 5. d dx To compute f(g(x)), first find f'(x) and…

A: Given Formulas we use:

Q: Use f-¹(f(x)) = x to determine a. Iff-¹(x) = - b. Evaluate f-¹ (8) is the inverse function of f(x) =…

A: We need to use the given property to solve the question.

Q: Find if the series converges or diverges.

A: The series ∑k=1∞​k3+1k2​ diverges.Explanation:To determine the convergence or divergence of the…

Q: A rectangle is bounded by the parabola defined by y=x², the x-axis, and the line x = 6 as shown in…

A: A rectangle is bounded by the parabola defined by , the x-axis, and the line as shown in the figure.…

Q: 2. The set of complex numbers can be defined as the set C = {a + bi | a, b = R, i²=-1}. For any…

A: Using the given definitions, we derive the proofs in parts a.), b.) and c.)

Q: Evaluate the following limits or show that the limit does not exist. 1. lim (x,y) -> (3, 3)…

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Q: Let f(x) = √1 − x over the interval [0, 1/2] . Find the surface area of the surface generated by…

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Q: a) Make a sketch of: f(x)= x², if x 2 Clearly label each part on your graph. You must use graph…

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Q: For y = f(x) = 7x4, find f(x₁ + Ax) -f(x₁) Ax = f (x₁ + Ax) -f(x₁) Ax 9 given x₁ =2 and Ax= 3. ...

A: The given function is To find:-  , given

Q: c. Car D must sweep out 27 radians to complete one full lap, and we know it sweeps out 7 radian per…

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Q: 12. a) b) Consider f(x) = and use, mtangent f(x+h)-f(x) h to = lim h→0 determine the simplified…

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Q: Find the indicated quantities for y = f(x) = 4x². f(4+ Ax)-f(4) (A) Simplify Ax (B) What does the…

A: To find the indicated quantities for .(A) To simplify  .(B) To evaluate part (A) as  approaches 0.

Q: If f (x) is continuous and 8 froa f(x) dx = 12, then find S²x² 0 x²f (x³) dx

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Q: For f (0): the period is For g(0): the period is For h(0): the period is radians and the amplitude…

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Q: 2. Consider the sequence 2,2 + √2,2 + √√2+√√2,2+√√2+√√2+ √2,.... Assuming that the sequence…

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Q: Evaluater(g(t)) using the Chain Rule: =(t) = (e¹, eº¹, −8), g(t) = 5t - 5 dr(g(t)) = { >

A: \)" data-mce-style="cursor: default;">r(t)=<et,e6t,−8> and g(t)=5t−5We have to find the…

Q: a. S 1 x(M - x) -dx

A: According to the bartleby guidelines we are supposed to do the first one of multiple questions…

Q: Find the length of the curve Length = y = =√₁² √₁³ — 1dt, √/t³-1dt, 1≤ x ≤ 4.

A: To find the length of the curve .

Q: Determine whether the statement is true or false. x². 5 x(x² +5) True False The function A can be…

A: The given function can be put in the form .The aim is to determine the given statement is true or…

Q: 14. Determine the equation of the tangent to y = x (x+3)² at x = -2

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Q: 3. Recall that a rational number r EQ is a number of the form r = where a, b & Z, b +0. Decide…

A: The objective of the question is to determine the truthfulness of the given claims and provide…

Q: Consider the functions: h(x) = f(g(x)) and Use the graphs of f(x) and g(x) to find the following •…

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Q: 3x √x +4 S dx (f) S 1 x(lnx)³ dx π/4 tan³ x cos³x (1) S™ dx

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Q: Q1. Find the general solution of the following differential equations and then find the particular…

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Q: = COS os(20) and h(0) = 3 cos(20), where is measured Letf (0) = cos(0), g(0) =

A: We are given,

Q: (e) ] 1 x2 _ 5+6 dx

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Solve the initial value problem. y'''-2y'' - y' + 2y = 0; The solution is y(t) = y(0)= 5, y'(0)=7,…

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Q: a. Graph the function ƒ(0) = 6 sin(0). 8 f(0) 6 4 2 -Jt/2 J2 π -2 -4 -6- -8 + Clear All Draw: MM…

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

Q: Given f(x) = 7 -5x, determine a. f¹(-4) + f-¹(-3) + f-¹(-2) Don't use the inverse function in your…

A: Given a function f(x), then Now, to solve part a, suppose to find  with out using inverse function,…

Q: Yaster Electronics manufactures and sells æ televisions per month. The cost and revenue in dollars…

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Q: 3. make cubic- polynomial function that 2 cross-3,6₁-21 has these

A: Given :- Zeros are : -3, 6, -2Now the cubic polynomial is given as f(x) = (x + 2 )(x + 3)(x - 6)Now,…

Q: Find the linear approximation of the f(x, y) = Answer: f(x, y) ~ X x + y at the point (1,4).

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Q: Find the point on y = 4+ x² that is closest to (1, 1). 0 (0,4) O (0.142, 4.020) O (0.545, 4.194) O…

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Q: Determine the value the constant a for which the function g(x) is continuous at x=1 9(x)=√x² +5x + 2…

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Q: Two capacitors (C₁ = 6.00 μF and C₂ = 10.0 μF) are now connected in series and to a 9.00-V battery.…

A: (a)    3.75μF (b)   V⁠⁠⁠⁠⁠⁠⁠1 = 5.625 V         V2 = 3.375 V (c) Q1 = 33.75μC      Q2 =…

Q: Consider the diagram shown below. Suppose that O 15.504 units long. (0, 0) and A = (3.8,0) and B=…

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Q: A company's total sales (in millions of dollars) + months from now are given by S(t) = 0.03t³ +0.5t²…

A: Given: To Find: To determine the units of  .

Q: 2) Find the volume of the solid generated by revolving the region bounded by the parabola y² = 4x…

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