Calculate the definite integral. 12 6 dx - 4 12 6. dx = (Type an exact answer.) - 4 X

Q: 41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an…

A: Explanation of the answer is as follows

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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Q: Find or evaluate the integral by completing the square. (Remember to use absolute values where…

A: ∫ (6x-8)dx/(x2 +2x+2) ∫ (6x-8)dx/(x2 +2x+ 1 +1) ∫ (6x-8)dx/((x+1)2 +1) ∫ (3(2x+2) - 14)dx/((x+1)2…

Q: Express the Cartesian coordinates (-3, 1) as polar coordinates. (2, 330°) O (2V2, 150) O (2, 150)

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Q: Find the potental function of the vector fieid F(z, 9) = -9yevi- 18zyej when the constant of…

A: Solving

Q: 1. Find the area of region bounded by the curves y = x² and line y=x. %3D

A: We have to determine area of region

Q: A 11. (2x- 3) dx 12 (+ 2x) dr SG²– 2) dr A -2 13. 1HIO

A: 11) ∫022x-3dx    A. -2 Explanation: ∫022x-3dx=2∫02x dx-3∫02dx                      =2x2202-3x02…

Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: V5 +3 v3 - E-2 where k is an integer to be found. V5 + V3 Without using a calculator, show that Cs…

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Q: Find the length of an are with parameterization r(t) = (-7 sin (t), -7 cos (t), -4). on the interval…

A: In this question, We will use the formula of the length of an arc of the parametrized curve.

Q: evaluate lim f (x) and lim f(x). X--00 -5 + 2e-* f(x) = %3D 5e-+6

A: f(x)=-5+2e-x5e-x+6limx→∞f(x)=limx→∞-5+2e-x5e-x+6             =limx→∞-5+2ex5ex+6…

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: Question 4 of 10 Find the volume of the solid that results when the shaded region is revolved about…

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Q: cot vo csc? Vo de 3 Vo² (4 + cot² Ve)

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Q: answer

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Q: What is the volume of the region R = ((x. y, z) e R'1 sxs 3:2 sy S 4:3 sz5 5)? %3D Select one: O…

A: Volume of the region R is given by volume=∫13∫24∫35dzdydx

Q: a) lim 3x + x2 x→1

A: We are asked to find the limit.

Q: A flu epidemic hits a college community, beginning with five cases on day t = 0. The rate of growth…

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Q: Let 7(t) = Find '(t) F (t) =

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Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: 1. ſ ev¤dx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 3.) Find the area bounded by the curve y = 2x and y =x-4 a.) Using Vertical strips b.) Using…

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Q: V4-x2 aluate dy dx using pol 2x-x2 prdinates.

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Q: Consider the following piecewise function: Find the values of the constants C and K that will make…

A: We have to find value of C & K

Q: Question * Given csc(0) = -2 and 0 E Quadrant III. Then the values of cot(0) and cos(0) are: cot (8)…

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Q: Determine the points at which the limacon defined by the polar equation r= 3 +2 sin e Has horizontal…

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Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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Q: 10

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Q: 'he graph of a periodic function f is shown below. f(4) 4 \1.57 3.14 4.71 6.28 a. What is the period…

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Q: 9) Local Linear Approximation a) Find the local linear approximation of g(x)= x° at x, = | b) Use…

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Q: ssignment : Determine the integral of the ff. functions 1. S- 6 dx 2. J5 х4 dx 3. S ( 4 x7 + 7 ) dx…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: By using the cylindrical shells method we have to find the volume.

Q: True or False (Mean Value Theorem): For the function f(x) = ÷+ V on the interval (0,9]. If f' (c) =…

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Q: Let R = {(x, y) ER214 < x? + y < 9}. By inverting to polar coordinates: %3D y? %3D Vx? - + y2 Select…

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Q: Given f'"(x) and f'(0) = 2 and f(0) 2x – 4 - 2. Find f'(x) = and find f(4) : =

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Q: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: The angle below measures 5.4 radians, and a circle is centered at the angle's vertex. 5.4 rad,…

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Q: Evaluate

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Q: 3 if x 1 5 4 5 -1 -1 -5 -4 -3 -2 2 3 4 -2 -3 -4 -5 Clear All Draw: 2] 2.

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Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

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Q: 1 2 dx

A: ∫9x12dx=9∫x12dxusing formula ∫xn dx = xn+1n+1here, n =12

Q: Find the indicated derivative. f (x) = (x³ – 5x + 2)(x² + x – 7); find f"(x). %3D

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Q: 5. sin x sin 4x dx c

A: We have to find integration value for the given function

Q: Choose point which has the correct location for the polar coordinate (2, 7). 90° 2 WIN 135° 4 7…

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Q: 7. S 8x³ e** dx il ww be 7dx 8. J sec x esinx bne

A: I am attaching image so that you understand each and every step.

Q: The Cartesian equation, x = 4, is equivalent to the polar equation, 1 = 4 cose 4 r = cose 43 r =…

A: Answer is in step 2.

Q: 13 dx 12

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Q: lim -1 x→0+

A: Separate the limit.

Q: Assume that $10000 is invested at an interest rate of 5% per year compounded continuously. (a) What…

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Q: Let E be the region in R that is under the plane x + 2y – z = 0, and in the xy- plane it is enclosed…

A: Find your answer below