What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD. y'= -1

Q: Which statement is true for a function f(x)? b The average value of a function is [ f(x) dx. a f…

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Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

Q: 9. S 1 x√64+9x² =dx

A: The given integral,      ∫1x64+9x2dx

Q: Find ди ds if w = sin(xyz), x = 1 - 3t, y=e¹-t, and z = 4t, find o

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Q: d [x² +1] dx x4 d dx -[(x² + 1)5⁰]

A: Topic = Derivative

Q: A kite flying 80m high is blown horizontally by the wind at a velocity of 5m/s. If the string is…

A: We are given that a kite flying at 80m height is blown horizontally by the wind at a velocity of…

Q: Evaluate the limit: sinh x2 – x2 lim x→0 sinhx − x

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Q: lim (sech 2x) csch x² +0x f(x) = csch x

A:

Q: I can't understand your solution.

A: Let's solve given integral.

Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: Topic:- application of integration

Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: 1. Let B = {. What is A. C. B. ( D. cannot identify } and the operation * is defined by the table…

A: To find what element we get after operating the given elements.

Q: Write the first five terms of the sequence, give the exact answer: {n+13) n=1 Determine whether the…

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Q: A rock thrown vertically upward at a velocity of 24 m/sec reaches a height of s(t) = 24t - 0.8t…

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Q: 4. x-1 x² + 5x+8 Ja da

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Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y =…

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Q: PLEASE SHOW COMPLETE SOLUTION.   Find the area bounded by y = 1/4 x^4 − x^2 and y = x(x − 2)(x +…

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Q: What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

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Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: B) Integrate the following Integral: Je²x sin 2x sin x dx

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Q: A. Find the area bounded by the curves, the axis and the given values of x. Sketch the graph. 1. y…

A: We are asked to find the area of the region bounded by the curve

Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

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Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x

Q: (a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: x≤ 1,0 ≤ y ≤ √1-x²,…

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Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: Use the first principles definition of the derivative to find f'(x) where f(x) = √x

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Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: v (2uv²-3) du + (3u²v² - 3+4v)dv = 0 Ov(u²v² +3u + 2v) = c 2 Ov(u²v² +3u-2v) = c Ov(u²v²-3u-2v) = c…

A: We need to solve D.E.

Q: 4x Find the average value of the function f(x): - 5 Submit your answer as an exact value. Provide…

A: Given problem:- Find the average value of the function f(x) =(4x/5) + 1 over the interval [-1,3].

Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

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Q: determine the parametric equations of the tangent axis to the ellipse x²/9+y²/4=1 at the point T =…

A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…

Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: 2. Given the graphs of f(x) and g(x) as shown, find: ✓✓✓✓ a) f(g(0)) b) f(g(2)) 67. -20 -2-

A: f(g(0))=? f(g(2))=?

Q: Explain why the function h is discontinuous at a = -2. 1 x = -2 h(x) = x + 2 1 x = -2

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)=pi/6. 1…

A: We use the concept of exact differential equations to find the general solution to given…

Q: √ x-1 x² + 5x +8 dx

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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Q: f(x)= 2x+5 3x-2 -19 (3x-2) f(x)=-

A: SOLUTION-

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: Given

Q: Evaluate the following integrals. 9x - 5 4. J dx 9x² 18x + 13

A: Given ∫9x-59x2-18x+13dx   Let  9x-5=αddx9x2-18x+13+β i.e.,    9x-5=α18x-18+β…

Q: fsec³ 7x tan5 7x dx 4.

A: Let's solve given integration.

Q: 2. Evaluate all of the integrals. a. [² sec²rtan r (1+sec x)² dz

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Q: Test for exactness then solve. (6x + y2)dx + y(2x − 3y)dy = 0

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Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y 0, and x = 49 is…

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Q: I. Evaluate the following limits. sinh x? – r 1. lim r→0 sinhr — -

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Q: I the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Topic:  application of integration