Consider fx sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4 1 O 1/2 3/8

Q: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

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Q: (B) Simplify the following expression sin (2 tan" x), then find the value of the following into sin…

A: 2tan-1x =sin-12x1+x2 .

Q: For f x 1/2 dx and using the substitution=x1/2, the resulting integral takes the form: -du 411…

A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

Q: What is the value of f(1) - 16B in | x³ Inx dx = f(x) ((1/4) Inx - B) + C? 00 O 3 0 2 01

A: This question can be solved using the concept of integration by parts.

Q: f(x) = 2x³9x² + 12x − 3 -

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Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

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Q: QUESTION 13 Find the area bounded by the trigonometric curves 3.667 square units 1.414 square units…

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Q: 1

A: We will solve the problem.

Q: 3x5 3x4+6x33x² - 6x Evaluate A B (C) (D) ·S= x²-2x-In x² - 4x 2 x² - 4x 2 x² - 2x 2 + In + In + In…

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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Q: f/² sin() cos() sin() dx (Consider initially the first 2 terms)

A: We have to find the integral.

Q: Investigate the given function and graph it accurately. 1. y = x²-x+1 x-1 2. y = In - -1 x+5

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Q: Evaluate 1 m+2 tan" (x) sec4x dx n (m + 2)(x) + — tan" (x) + C tan m 1 -tan (m+3)(x). ī -tan…

A: Solution is here

Q: -S₁ Consider 08 14/3 O 17/8 05 3x5 3x4+6x³-3x²-6x •√(x-1 -dx- Using the method of partial fractions,…

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Q: QUESTION 16 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

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

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Q: (5 Lim 9-5 dx S a -x²-8x-15

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Q: b. Identify the function's local and absolute extreme values, if any, saying where they occur. -15…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: The objective is to find the slope and equation of tangent line.

Q: 2 I зах 9x²-6x+5

A: On solving this we will get

Q: Solve the following differential equations: 2 √1-y² (a) - dx + y sin 2x -dy = 0 cos 4x+1

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Q: Consider I x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4…

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Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: 4 The slope of the tangent line to the curve y = X at the point 5, is: 5

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Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?     3/8…

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

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Q: Find an equation of the line tangent to the graph of f(x) = (4x-3)(x+2) at (1,3). The equation of…

A: topic- equation of tangent line to the graph

Q: S The integral S x dx x²+√√x²-1-1 sece tane de sece - 1 sec²0 do 1+tano cose dᎾ 1 - sino sine de 1 +…

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Q: Question Find the area of the region that is bounded above by the curve f(x) = (x - 1)² and the line…

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Q: Let S be the solid inside the sphere p _ 6cos@ and below the cone Ø = π/4 Find the volume of the…

A: S be the solid inside the sphere ρ=6cosϕ and below the cone ϕ=π4

Q: eading due north at 500 km/h. If it encounters a wind from the northeast at 1 sultant velocity…

A: We will solve the problem.

Q: 3x5 dx Using the method of partial fractions, the given integral can be written as 3x² - 6x Consider…

A: To solve the following problem

Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: ·S= cost cose de . 1-sino sece tane de sec-1 The integral sine de 1+ cose sec²0 de 1+tano x dx can…

A: Let's transform integral by using trigonometric substitution.

Q: 2 J xe9x da 0

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Question 3 To evaluate (B fr²cost sx dx use integration by parts. What is the expression after the…

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Q: Question 9 The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x…

A: Solution is here

Q: Pre Estimate the slope (slope = rise/run) of the tangent line to the curve. Q st 6 8 P 9 6 64 4 62 4…

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Q: Question 6 6dx For the method of partial fractions, to evaluate S90 -1 = S Adx + S = X-1 Bdx X+1'…

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Q: Consider the function f(x) = x² - 9x + 20 x - 3 a. Find the first derivative. f'(x) = b. List any…

A: We have to find the derivative and monotone intervals.   According to our guidelines we can solve…

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: S For x1/2 dx and using the substitution = x1/2, the resulting integral takes the form: x-x3 -du S-…

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Q: QUESTION 3 Evaluate sin(Inx sin (Inx) dx Integration by parts will be used repeatedly. What is the…

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Q: Question Find the area A of the region that is bounded between the curve f(x) = ex-2-3 and the line…

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Q: Question Find the area of the region that is bounded above by the curve f(x) = (x + 8)2 and the line…

A: This question can be solved using the concepts of area bounded by curves.

Q: ve [No.5] -2 2 зах 9x²-6x+5

A: On solving this we will get

Q: 11. Evaluate 1 (a) √x (x² +1)³dx, (b) fdx (c) fda (d) fx x+2 ev dx √x²+4x IT'

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Q: Newton's Law of Cooling a) A cup of coffee has temperature 95° C and takes 30 minutes to cool to 61°…

A: SOLUTION-

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

A: Solution is here

Q: Use cofactor expansions to evaluate the determinants in Prob lems 1-6. Expand along the row or…

A: Please see the answer below.