T₁ 0 1+e²x dx Hint: e²* = (e*)²

Q: +√³1 (2) dx = -3 and ³ S If it is known that [²₁ √f (a) da = 4, find the value of f(x) dx.

A: To find out the integral value.

Q: Evaluate x/12 0 14√/1- cos 12x dx.

A: Given, ∫0π4141-cos12xdx

Q: Show that there are no tangents to the curve f(x) = 6x3 + 2x2 that have a slope of -5.   Please…

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Q: A region bounded by f(x) = 5 — x, y = 0, and x = 1 is shown below. Find the volume of the solid…

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Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: To find volume V of the body formed by revolving the given region .

Q: Solve the following initial value problem completely, and check your answer by comparing it to the…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x³ - 18x²…

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Q: 4. Find the area of the region bounded by y=6-2-2² and the z-axis. 125 (a) A= square units 6 (b) A =…

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Q: The following differential equation (+1)² + ² = sin a dy dx x has an order of 0 0 O 3 O 1 02

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Q: 11. Integral sin³ R cos R dR

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Q: Consider f(x)=x*. Find the first derivative, f'(x).

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Q: Determine the area enclosed by y = from x= -3/2 to x = 1. |- 1 x+2 and y = (x + 2)²

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Q: If it exists, find Answer: x³ - ze²y lim (x,y,z) (-1,0,4) 6x + 2y3z' Write DNE, if the limit does…

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Q: What is the area of the region in the first quadrant bounded above by y = -2x + 8 and below by y =…

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Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: Let F(x) = [² costdt. Find F'(x).

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Q: Refer to the functions r and p. Find the function (p-r) (x) and write the domain in interval…

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

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: Using the Inverse Function Theorem, what is (-1) (8) given that /(x)=√6x-2? Note that (11) = 8. (Do…

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Q: Find the general solution of the differential equation y" — y' - 12y -32t + 24t². NOTE: Use t as the…

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Q: 6. (a) f(x) = arctan (e-2) 6. (b) f(x) = [arcsin (²)]³

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Q: A region bounded by f(y) = 2y + 3, y = 1, y = 3, and x = 1 is shown. What is the volume of the solid…

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Q: hid. The line y d. The line y = -5/8 -5/8 redbuthents 2 y 0 X = ochiul 14 4 X = - y² 2 1 y² dibel 2…

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Q: 10. Integral 2-t dt

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Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Given the functions: f(x)=x²³-8x g(x) = √2x h(x) = 6x+7 Evaluate the function h (f(x)) for x = 3.…

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Q: Using the Inverse Function Theorem, what is (-) (8) given that f(x)=√6x-2? Note that (11) = 8. (B8…

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Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

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Q: Find the coordinates of the points of inflection for the function. 14) f(x) = 7e-x²

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Q: Find the value of E, the margin of error, for c = 0.99, n = 15 and s=5.4. OA. 1.072 OB. 3.659 O C.…

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Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

A: The solution is given below

Q: Given the functions: g(x) = |x-2| Evaluate the function (h-g) (5) for the given value of x. Write…

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Q: = A region bounded by f(x) 9 8 Find the volume of the solid formed by revolving the region about the…

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Q: Find the largest product the positive numbers x, y, and z can have if x² + y + z = 4. The product is…

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Q: Find dy/dx if y=2 – x^2.

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

Q: Evaluate f 10x(x² the following antiderivatives + 5) 7dx

A: The given integral is;  10x(x2+5)7.

Q: Find the average value of: f(x) = 8 sin x + 3 cos x on the interval [0,1] 3 Average value =

A: Solved below.

Q: Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint,…

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Q: Find the domain and range of the following function: f (x)  {(2,3),(3,4),(5,7),(10,3)}

A: Given: f (x) = {(2,3),(3,4),(5,7),(10,3)}

Q: Write an equation for the function graphed below. The y intercept is at (0,0.2) y = 5 -4 -3 2 -- 1 4…

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Q: Q/. Find the limit of the function * lim 4-√x²³+7 3 X

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Q: Which one of the following diagram represents: AC CBC a. C. Ό B B B

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Q: Show if the sequence converges or diverges using  L'Hôpital's rule…

A: A sequence is said to be converge if its limit  exists, otherwise diverges.L'Hospital rule:- If…

Q: Evaluate the following antiderivatives. f (x sinh x + 1) dx

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Q: Find the solution of the initial value problem y" + 6y' + 10y = 0, Y (²7) = 0, y¹ (7) = 9. 2 y(t) =…

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Q: Find the location and value of each local extremum for the function. 28) + -3 3 -4 -M

A: To find location and value of each local extremum of given function.

Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

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Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fraction…

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Q: Find the indicated limits, noting L'Hôpital's Rule wherever it is used. lim (1-ª)* (constant a)

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