Determine the indefinite integral 6.xV-5]7 dx by substitution. (It is recommended that you check your results by differentiation.) Use capitalC for the free constant.

Q: If u(t) = (sin(2t), cos(5t), t) and v(t) = (t, cos(5t), sin(2t)), use Formula 4 of this theorem to…

A: We will find the dot product.

Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: If u(t) = (sin(7t), cos(7t), t) and v(t) = (t, cos(7t), sin(7t)), use Formula 5 of this theorem to…

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Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

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Q: Evaluate the definite integral. i+e"j+t – (e~1 – 1) j + 5 i-ej+: (e – 1) i – (=" – 1) j + -1)j+극k i+…

A: We have to find the solution of  integral

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A: As the equation is homogeneous , put y=vx and solve .

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A: We can sole this as follows:

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A: Solved below.

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Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: ve the given ODE using Laplace Transform a. y" – 4y' + 3y = 6t – 8 ; y(0) = 0, y'(0) = 0 -

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Q: O Find the volume of the solid under the surface z = xy and above the triangle with vertices (1, 1),…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Determine whether the sequence converges or diverges. If it converges, find the limit.

Q: -ide each of the fol x-4x²+2x-3 x+2

A: Solve the following

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Exact Equation ( 2% ty cos x) dx + sın x dy = dy = 0

A: The given differential equation,      2x+y cosxdx+sinx dy=0

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A: Given query is to expand the logarithmic expression.

Q: f(x) f'lx) %3D

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Q: Find the limit. If the limit does not exist, type DNE. 2z – 2ry? = lim (1,9) → (-1,1)

A: We will find the limit.

Q: b)Let f(x)= 2(x-4)(x+1)/(x-1)(x-3) 1.find all the intercepts 2.Calculate and write the equations of…

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Q: PART 1. Complete the table Tre Lf (x) f (x) f'(x) f'(x)dx (2) (1) f(x) = 3x* – 5x³+ 6x2 - r + 7 (1)…

A: The given function is  f(x)=3x4-5x3+6x2-x+7.

Q: 5 tan a If f(2) = f'(x) - then f'(3) = %3D

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Q: Question 9 > A 25-year-old woman burns 800t cal/hr while walking on her treadmill. How many calories…

A: Solution: Given  Function of calories are  burned= 800t cal/hr  So for 3 hrs  t=3 So calories burned…

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Q: Find all values x=a where the function is discontinuous. For each value of x, give the limit of the…

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Q: Find the exponential model y = ae bx that fits the points shown in the table. 3 y 6. 1.5 y = 2e°…

A: In the given problem we input the value of x and get the value of 'a' & 'b' with the help of…

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A: Solve the following

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A: Calculate intensity I. Given I0=1, R=8.25 Richter scale Formula: R=log(I/I0)

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A: Here, let h be the height, l be the length and w be the width of the box. Then given that height, is…

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Q: Which of the following are equivalent to log, (4)? Choose all that apply. 1 log, (16) log, + log,…

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Q: Evaluate the following limits. If needed, enter 'INF' for o and '-INF for -o. (a) V6+9x? lim x-00…

A: Solve the following

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Graph the function. f(x) = 3*

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Q: omplete the table for the radioactive isotope. (Round your answer to 2 decimal places.) Half-life…

A: We have to find out the amount

Q: The equation y = log(x – 3) has a vertical asymptote at: X =

A: The graph of log(f(x)) has a vertical asymptote at the value of x such that f(x)=0.Example: for…

Q: Consider the function f(x) = 6x? – 10x + 8, 0 < x < 9. The absolute maximum of f(x) (on the given…

A: Explained below

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A:

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A: Given linear system is Xa=Y is having no solution. Suppose that X be f by g, where f&gt;g. X is full…

Q: average rate of change

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Q: Find the arc length of the graph of r(t) = ev2ti +ev2tj+ 2tk, 0 <t < v2 ln 4 NOTE: Enter the exact…

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Q: The area of a square with sides of length s is given by A = s'. Find the rate of change of the area…

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Q: Let f(2) = - 8 cos x + 9 tan e f (2) = (-) = C 4

A:

Q: Find the cost function if the marginal cost function is given by C'(x)=x 1/2 + 5 and 9 units cost…

A: The marginal cost function is given by,   C'x=x12+5

Q: (a) Consider A B + X-1 7x2 - 17x + 38 C (x + 6)(x – 1)²- x+6 (x – 1)² (i) Use partial fractions to…

A: (7x2-17x+38)/[(x+6)(x-1) 2]=A/(x+6) +B/(x-1) +C/(x-1) 2

Q: Evaluate (if possible) the sin

A: answer is in next step

Q: Consider the functions below. f(z) = VT – I g(z) = r² +1 Find each of the following, if possible.…

A: Given query is to find indicated composite function.

Q: Find f by solving the initial-value problem. f'(x) f(9) = 45

A: