QUESTION 1 In x Complete the following table to evaluate the limit lim X-00 √x Step Explain the step Inx lim x-+00 √√x Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 11 18 lim X-00 11 010 = lim = = 0 2√x lim X-00 X 18 1 2√x 2

Q: QUESTION 4 To evaluate x²cosx dx' use integration by parts. What is the expression after the second…

A: The given integral is: I=∫x2cosxdx   Apply the integration by parts to solve the above integral.…

Q: sin (In. sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

A: We need to integrate the given function with integration by parts.   We will do it twice

Q: dx 2. The integral S can be transformed to which of the following when trigonometric (x²+4)²…

A: Please see the answer below

Q: R 5″ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=- 4 4 (A…

A: Here we have to find the area bounded by the given trigonometric curves.

Q: The volume of the solid generated by revolving the region bounded by x2-4y and y2 = 4x about b using…

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Q: Evaluate the following. 1. [(sec 3x+cos3x)² dx

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Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ( (1/4) Inx - B) + C? A 3 (в 0 с 2 D 1

A: We have to find the value of f(1) -16B where it is given that  ∫x3lnxdx = f(x){(1/4)lnx - B }+C    @…

Q: Question 18 Find the area bounded by the curve y 8 square units 4 square units 16 square units 10…

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Q: If a particle moves on a straight line so that s = et (cost – sint) . Which expression can be used…

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Q: Find ·S= y dy 0(√3+2-5) (5√3+2-1+24)+C 0² (√y+2-5)(-5√/y+2+y+21)+C 03/(√3+2-5) (5√y+2+y+21) +C…

A: On solving this we will get

Q: Find 36 zdV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), and (0,0,2) E

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y² = 4x about y = 4…

A: Using circular ring method about y=4 find outer and inner radius then evaluate volume

Q: ad Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: We have to solve the trangent line y

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: Which of the following equations is 1011th derivative of h(x) = -5 cos x ? Oh(1011)(x) = -5 sin…

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Q: fsinx cos/x Зл А 256 3 (В 512 (C) None Зл (D) 512 3 E) 256 -dx is equal to

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Q: 6 Ⓒh'(x) = 7(7x³+4x) (21x² + 4)

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Q: 9. [cos° { xsin’ } xdx

A: The objective of the question is evaluate the indefinite integral.

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Given the spherical tank with diameter 4m So the radius of the spherical tank R = 2m Weight density…

Q: 14. Solve the initial-value problem dy dt = -2y + u₂(t)e¯¹, y(0) = 3.

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Q: Suppose m and n are constants and m‡ n.- Evaluate [sin(mx) cos(nx) dx 1 1 -cos(m-n)x. cos(m+n)x] +C…

A: To find the value of given integral.

Q: 14. sec xdx 2 3/2 (1 – 4 tan x)³/²

A:

Q: QUESTION 4 Evaluate › [ sin(lnx) dx' Integration by parts will be used repeatedly. What is the…

A: Integration by parts

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: Evaluate sin sin (Inx) nx) dx Integration by parts will be used repeatedly. What is the expression…

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Q: (e) x = = 2y², x = 4 + y² - (f) x = 1 — y², x = y² – 1 32 Answers (a), (b), (c) In 2-1, (d), (e)…

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Q: (-2-x)²+5 if x ‡ - 3 = 4x + 17 if x = -3 the following limits. Enter "DNE" if the limit does not…

A: The given function is: f(x)=(-2-x)2+5 if x≠-34x+17 if x=-3

Q: 3x5 ·S -dx- Using the method of partial fractions, the given integral can be written as 3x4+6x³3x² -…

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Q: Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the expression after…

A: Given ∫sin (ln x) dx Let I=∫sin (ln x) dx By using integration by parts method,∫udv=uv-∫vdu u= sin…

Q: 12. S e 3In(2x-1) 2x - 1 - dx

A: The given integral is: I=∫e3ln2x-12x-1dx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: S- Find y dy Vy+2 using the substitution u +5=√√x+2. A ²/ (√x+2-5) (-5√/y+2+y+21)+C ℗ ²/(√√y+2-5)…

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Q: Question 8 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Solved below.

Q: For each function graphed below, state whether it is one-to-one. Graph 1 Graph 2 8- 4- 6+ 2+ 4-…

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Q: Find the area bounded by the curve 4 square units 10 square units 8 square units 16 square units 3 y…

A: Area

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

A: We have to calculate the area of the smaller region bounded by x+52=2y from left sides,and bounded…

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: 3x5 ·S= 3x4+6x³-3x² - 6x x²-2x-In -1 [ + €². (x-1) 1/6(x+2) 16/3 (x+1) 1/2 +C x² - 4x (x − 1)…

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Q: Convert S.S. dzdydx 3-√√9-**-* Into an integral of spherical coordinates 319-x2

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Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

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Q: To evaluate x²cosx dx' x2sinx – 2x cosx+2 x2sinx – 2x cost – 2 x2sinx+2x cost – 2 x2sinx+2x cosx – 2…

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Q: A spherical tank of diameter 4 m is half-full of water (weight density - 9800 N/m³). Setup the…

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Q: a) For any given function y = f(x), explain, with words, how you would determine whether or not…

A: To explain : The inflection point of a function.

Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: For x 1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du 4-u U…

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Q: 20. For A. B. C. D. S x1/2 dx and using the substitution u=x1/2, the resulting integral takes the…

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Q: dx 3-2x-x²

A: We need to solve : ∫-10dx3-2x-x2

Q: Consider S[x-m+ A) 5 B) 14/3 C) 6 D) 17/6 ·S= 3x5 3x4+6x33x² - 6x A B C + + x-1 x + 1 x+m -dx. Using…

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Q: 4. What is the value of f(1) - 16B in § x³ Inx dx = f(x) ( (1/4) Inx - B ) + C? A. 0 B. 1 C. 2 D. 3

A: We know that integration of xn is xn+1/n+1.   Here i attached the solution of this question.

Q: dx 3-2x-x²

A: Evaluate the following

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: The simple use integration