d: (a) lim ズー2 オー2--(*+1)

Q: Evaluate the integral .8 xV x+1 dx

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Q: explanations

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Q: The 26th term of a Fibonacci sequence is 121393 and the 27th term is 1916418. What is the 24th term?

A: F0=0, F1=1Fn = Fn-1 + Fn-2,  n≥2 F26 =121393F27 =1916418F27 =F27-1 + F27-2F27 =F26 + F25F25 =F27 -F2...

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A: topic - trigonometric identities

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Q: Evaluate * cos (e + a?) dx 24 +1

A: To find: The integral ∫44cose3x+x2x4+1dx Concept used: ∫aaf(x)dx=0

Q: has

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Q: 10. x= cos't; y sin't

A: To find the second derivative.

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Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.002x° +0.07x + 14x + 60...

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Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd . 

Q: 3. A piece of sheet metal, 100cm by 50cm, is to be used to make a rectangular box with an open top b...

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Q: CHAIN RULE DERIVATIVES Directions: Differentta te the given fanctions gx)-13bc°(56+ 4c t 9)°

A: To differentiate: the function g(x)=131x35b+4c+95 Formula used: Chain rule of differentiation ddx(f(...

Q: Show that the equation x – 18x + c = 0 has at most one root in the interval [-2, 2].

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Q: Sketch the level curves of the function f(x, y) = y – 3x² for c = 2. 8+ 5- 4 2 -6 -5 -4 -3 -2 -1 4 -...

A: Explanation of the answer is as follows

Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

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Q: In how many ways can John, Leo, and Mike be seated in a row? a. 3 b. 4 c. 5 d. 6

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Q: 6. Evaluate the improper integral 3dx. Use limits as needed. Give exact 2 answer. . 3

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Q: xcos³x² The S dx is 1-sin x? sin?x² + C {c}sin x² +sin²x² + C {D}sin x? –sin²x² + C { A} sin x² 2 4 ...

A: This question can be solved using integration by substitution.

Q: 6.2 o, 417 り O• 2 o.447 X, o. 587 0.3 nd:. う、= ?

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Q: (14) = (x – y + 5)? dx dy %3D dy (15) (x² – y²)" – xy = 0 dx dy (16) 2xy = x² + 2y² %3D dx

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Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: I. Solve the following: 1. Given: y 2x - Find: a.) dy/dx b.)y" 2. Given: 16y – 9x = 144, find y"

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Q: Anote card company has found that the marginal cost per card of producing x note cards is given by t...

A: Given query is to find the cost of prducing x cards.

Q: Use the Integral Test to determine if the series 1 Σ (n +2)°/¾ n=1 converges or diverges.

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Q: xtra questions: Find the Derivative of 8 1. y = 10 vx ++ x2 2. y = ta n(si n x) 3. у %3D cot?3x

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Q: A solution to the trigonometric equation 2 sin² x = 2 – - V3 cos x i. 90° ii. O° iii. 30° i only i a...

A: Given: 2sin2x=2-3cosx   As we know that; The Pythagorean identity; sin2θ+cos2θ=1    

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Q: Tork Problems [. Evaluate the integral xV x+1 dx

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Q: y- (6+5t-ビア 3.

A: We can find the derivative using chain rule as below

Q: 2x-2y* If f(x,y)={3x² +3y² if (x, y) # (0,0) then: m if (x,y) =(0,0) f(x,y) is continuous at (0,0) i...

A: To check whether the function is continuous or not. Given information: The function is f(x)=2x4-2y43...

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A: We have to find the limit of the sequence and find first five terms

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Q: using seperation of variable method, solve dy/dx=x3y2

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Q: Work Problem 1 Evaluate the integral 13 (x+3)°dx

A: Topic = Integration

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Q: x +1 limx→∞ х3 — 1

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Q: Evaluate the Integral 3sin2ß) 4 cos2ß dß. A 30 - (4 – 3sin2f) 5 + C (4- 3cos28) 5+ C B 30 -(4- 3cos2...

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