The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

Q: D 2x³ – x² + x +2 = (: find dx - A+B+C+D- Consider - + + + x+1 x4 + x3 O 2 O 4 O 3 O 5

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Q: Let r = xI + yj + zk and r= |r|. Find each of the following. (Give your answers in terms of r.) (a)…

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Q: Question 1 Consider / sin*x cosºx dx. f we let 4 = sin x, the integrand can be transformed to, (B ®…

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Q: If i x w = i- j+ k, and i · w = 4, and 0 is the angle between i and w, 2 - (a) tan 0 = (b) 0 =

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Q: Evaluate the integral 8) da 21 3-8. by making the substitution u = NOTE: Your answer should be in…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given,   r(t)=cos(πt)i-ln(t)j+t-16k

Q: Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 6 that pass through the point…

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Q: 2х — 1 - dx 6х + 18 x² -

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: ∫f(x) dx=∫ 5-31+x2-1dx=∫ 5dx-∫ 31+x2-1dx=5x-3arctanxAdd a constant to the solution=5x-3arctanx+C…

Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

Q: (2x + 4) + 1 dx- x² + 4x + 5 x² + 2x– 10 2 (2x + 4) + 1 2 Consider dx = x2 (x² + 4x + 5) dx.…

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Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: We need to evaluate integral.

Q: 3x2+ 8x – 12 3. -dx. Use partial fractions. x3+7x2+ 12x

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Q: 4. x2(y + 1)dx + y² (x – 1)dy = 0

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Q: 1. Evaluate the following limits. 4x – 7 lim C. +-1-3r – 2r + r + 1|

A: Let's find.

Q: dy 4у dx х (у-3)

A: Given query is to find the soly of the differential equation.

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: Given problem:- Does the function satisfy the hypotheses of the Mean Value Theorem on the given…

Q: 5x (x² +a) dx is In +eTan-1X The resulting integral of + C, where a, b, d, and e are integers. What…

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Using Integration By Parts, x3 Vx² + 4 dx = u v- -Svau - Svdu- بی تر ر ترا Find UV- 3 1 .x2 (x2 +…

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Q: 12. The slope of the curve y = x2 - e-* at its point of int A. -In 2 В. C. 2+In 4 D.

A: Given query is to find the the slope at inflection point.

Q: 4x3 + 4x? – 2x + 4 dx - (x² + 1)?

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Q: dx - [f(e)de find f(e) - S. (x² + x + 1) 2 Using Trigonometric Substitution O 3 sec? e 4 4 3 sec? e…

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Q: x² + 4x – 5 dx = Using Trigonometric Substitution :| f(e)de find the new limits of integration. x+2…

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Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: 12x²-x² * x+2 dx= D dx • x +1 Consider dx = ,find A+B+ C+D· x4+ x3

A: Consider ∫2x3-x2+x+2x4+x3 dx=∫Ax+Bx2+Cx3+Dx+1 dx, then to find A+B+C+D.

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: You’ve started a small business selling handmade keychains. You’ve given one frequent customer the…

A: Here, the given function for the price is: p(x)=10-x2

Q: MY INOTES ASK YOUR TEACHER PRACTICE ANOTHER Two people start from the same point. One walks east at…

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Q: f(x) – f(7) g lim x-7 x - 7 se symbolic notation and fractions where neede

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Q: Find f'(x) and f'(c). Function Value of c f(x) = (x + 4x)(5x + 2x - 4) C= 0 %3D f'(x) = f'(c) =

A: A detailed solution is given below

Q: dx Using Trigonometric Substitution J- 4 sin 8+C express the answer in terms of x. (x²+ x + 1) ² 4x…

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Q: x³ + 6x² + x +2 dx? How many quadratic and distinct factors are in the denominator of x³ +1

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Q: Find the two x-intercepts of the function f and show that f'(x) =0 at some point between the two…

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Q: Find a and b in Va+4x-5 dx = x+2

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Q: 2) Convert the following rectangular equations to polar equations. a) x² - y = 3y b. 9xy = 1

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Q: company's revenue from selling xx units of an item is given as R=1500x−x^2 If sales are increasing…

A: Topic:- application of derivatives

Q: 6 (a) At point Q, fx is ? fy is ? and (b) At point R, fx is ? • and fy is ? (c) At point S, fx is ?…

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Q: Evaluate the indefinite integral sin v cOs vdv

A: Given:       ∫3sin4v cosv dv Taking constant out.         =3∫sin4v cosv dv substitute u=sin…

Q: 2n+1 5. Σ 'n°(n+1)² n=1

A: let  bn=1n3∑n=1∞1n3    is convergent   by p series  Recall ∑n=1∞1nP    is convergent  iff p>1

Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

A: If f'(x)>0 for every x on some interval I , then f(x) is increasing function . If f'(x)<0 for…

Q: 4. Given [2r + 5], if r2 I = -1 and at r = 2. If discontinuous, classify the type of a. Discuss the…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i + 10 sin(t)j +…

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Q: sin(3x)cos(3x) sin(2x) 의[cos(2x)-1]+ +C 12 8 4

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Q: sec(3r2 + In 2) evz+2 +9 a. y =

A: Use simple differentiation formula.

Q: What change of variables is suggested by an integral containing * V25 + x²? O a tanø O none of the…

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Q: f2x² Find uv- v du Using Integration By Parts, dx =uv- du UV- | S12 xe 6 x2 dx 3 x2 6x e dx 02

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Q: Select all that apply: □ (5. 똥) □ (5. 플) O (5. -*) (-5, ) □ (-5. 똥) O (-5, -)

A: Polar