dx , find f(0) · Using Trigonometric Substitution 3 (x²+ x + 1) 2

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

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Q: Find the second derivative. 14) y = 4x² + 12x + 4x-3

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Q: Eveleate inter ssin(2x) dx

A: We can find the integration as below.

Q: 9- 4x2 Evaluate: xp-

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Q: a Derivative In Exercises 59-84, find the Finding derivative of the function. 60. y = (x² – 6)3

A: Topic = Derivative

Q: Region bounded by: y = x+1, y = -x + 4, x = 0 Rotate about: y-axis %3D

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Q: Question 8 If limx→a J(X): |8(x) lim;-»a [f(x)] = = 1 and limx→a g(x) : = o then, we must have %3D…

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Q: 48. f(x) = (x – 4)(x² + 6x – 1), (0, 4)

A: We need to find the equation of tangent line for fx=x-4x2+6x-1 at point  0, 4

Q: each of the problems, solve the given differential equation. 3. y` + y2 sin x = 0

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

Q: [2x+11 3 1 dx . evaluate Consider 3 1 dx x+3 dx = x2 + x- 6 x- 2 | x+3 X- 2 x+3 x- 2 In +C x+3 In…

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Q: Finding a Derivative In Exercises 31-44, find the derivative of the function. sin x 36. у %3D

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Q: Using Integration By Parts, x Arcsec 3x dx = u v- |v du

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: 00 n +7 Use the ratio test to determine whether>. converges or diverges. 7" n=3 (a) Find the ratio…

A: To find whether the given series converges or diverges using ratio test.

Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

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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: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

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Q: Question 1 Which of the following are subspaces of R ? Choose all correct answers. {(x, y, z) E R³ |…

A: Only option 1 and 3 are subspace of R^3

Q: A Hippogriff is a magical beast that had the front legs, wings, and head of a giant eagle and the…

A: answer is in next step

Q: ;dx

A: Given query is to find the value of the integral.

Q: Sveluate esing Sub method 7.

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Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: A shot putter threw an 8 Ib 13 oz shot 62 ft, 2 in. Assuming the shot putter launched the shot at a…

A: answer is in next step

Q: 2x3- x² + x + 2 D dx X +1 C Consider find A+B+C+D x4 + x3 y3 4 O 2 O 5

A: We can solve as follows

Q: find S- とx 1-COS2X

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Q: Evaluate the integral cot5 x csc3x dx O Lesc" x - ese" x + cse" x - c 2 csc' x + 5 글csc3 x + C 1 X +…

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Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x? + xy + y? - 9x…

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Q: Answer the following questions for the function f(x) = a/a² + 9 defined on the interval – 6 <a < 7.…

A: According to the guidelines, I am answering the first three subparts. Please repost the remaining.…

Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

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Q: Find the derivative of y. 30) y = In (sinh 5x) D . sinh 5x A) coth 5x B) 5 csch 5x C) 5 coth 5x

A: We can answer the question as below.

Q: Evaluate Sum 80

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Q: *(5t² – 3t=3) dt

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Q: 3. Let h(x) be a twice-differentiable function with h' (x) <0 and h" (x) <0 for all real numbers x,…

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Q: 4 x² + 4x - 5 Consider using Trigonometric Substitution find x . x +2 sec e O 3 sec e O -2+ sec e O…

A: We have to choose the correct option from the given options according to the given information

Q: Question 8 Saved If limx→a f(x) 8(x) = 1 and limr-→a g(x) = 0 then, we must have limx→a = True False

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Q: (æ² + 1)² x²ez² 2(x2 + 1) + C x²ez? 2(z² + 1) -ze +C O A Ов 1 2(x2 + 1) cea 2 2(2² + 1) - 2" +C…

A: The given integral is: I=∫x3ex2(x2+1)2dx=∫x2ex2(x2+1)2x dx Substitute x2=u⇒2xdx=du⇒xdx=du2 So,…

Q: Prove the identity. 1 + tanh(x) – e2x 1 - tanh(x) 1 + cosh(x) 1 + tanh(x) 1- tanh(x) 1 - cosh(x)…

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 6x + 1, [-1, 2] minimum (x,…

A: Finding extrema of a function. We can find the extrema of a function of function f(x) by  finding…

Q: Se dt

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Q: 17) Water is falling on a surface, wetting a circular area that is expanding at a rate of 5 mm²/s.…

A: Explanation of the answer is as follows

Q: х х sin sin2 cos 2 dx. 2

A: Given integral : I=∫0π2  sin2x2  cos2x2   dx

Q: У(2 — 2х)100 — у — хz; ху and yz.

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Q: 5xy = 4x?z – 3yz?; yx and yz. -

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Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: Given t = x + ex, find dx/dt

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 dx x(xА + 2) Need Help? Read It

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A: Given function F(x,y)=( 2x-6y ) i+(-6x+14y-7) j

Q: 15х2—х3— 43х — 19 Ax + B C The integral /- D + rx +s -dx can be rewritten as dx. (x+1)2(x²– 6x + 13)…

A: The integral ∫15x2-x3-43x-19x+12x2-6x+13 dx can be written as ∫Ax+Bax2+bx+c+Cmx+nt+Drx+s dx.To…