ropriate substitution, n³ (4x)cos*(4x)dx is equal to

Q: 2+ and g(x) = Figure out the domain of (fog)(x) in which f(x) = 4-x2

A: Given f(x)=2+x4-x2g(x)=1xHere…

Q: Match each graph type with its corresponding function.

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Q: 7/2 SAT sin" x cos3 x dx

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Q: Let F(a) = f(x*) and G(x) = (f(x))". You also know that a = 2, f(a) = 3, f'(a) = 15, f'(a*) = 2 |3D…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 9 cos(t)i + 7 sin(t)j +…

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Q: xArctanx - Invx² + 1 = y

A: Topic:- derivatives

Q: Solve the second derivative(y") of the following

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Q: x3 (x2 + 1)3 dx

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Q: dx (x² + 1)

A: To solve the given integral

Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: 8. The rationalizing substitutionw + 4 = u² transforms - dw into w+4 A. fu² - 4°du B. 2fu² - 4}du C.…

A: Given: I=∫w2w+4dw  ...1   As we know that; The Power law: ddxxn=nxn-1 And ∫a·fxdx=a·∫fxdx , where a…

Q: (-1) -1 Given the alternating series E Which one of the following gives n1 5+3n b? n+1 Select one:…

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Q: fintthe XP COS ५: टे. 8 e

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Q: Find the general solution of the given ODE * (y² – y) dx + x dy = 0. - y=c 5 +4x + k Option 1 Option…

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Q: 5. In the accompanying diagram, BA is tangent to circle O at A. Radii OA and OC are drawn, and OC is…

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Q: |Q1/ Find the transpose for A(3×4) matrix. Q2/ Add two (2×2) matrices and put result into new…

A: We have to find A' and A+B

Q: The Cartesian equation, x = - 4, is equivalent to the polar equation, O. 4 cose Or2 = 4 cos e %3! I…

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Q: A. Solve the following problem involving derivatives 1. The position of a particle is given by the…

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Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: a) Explain why the function f(x) = e#² is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The integral 2 X dx | - Vx2 – 4 3 1

A: The objective of the question is evaluate the definite integral.

Q: Find the limit. (ti – 6j + r² k) lim t→4 lim (ti – 6j + r² k) = i+ j+ i i i k

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Q: convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n…

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Q: Find the equation of the tangent line at the given point on the curve. 327x 3x² + 3y² , 109y 2 10…

A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where, m is the…

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: S cosh(5x – 7) dx

A: The given integral is:∫cosh5x-7dx

Q: Exercise 2. Find the following limits 3x +1 1-3x² 3x +1 1) lim to 2x + 5 2) lim X+ 2x +5 3) lim x-…

A: Use limit concept

Q: The solution y, of the homogeneous differential equation y(4) + 36y" = 0 is None of them c_1+c_2…

A: We have to find solution

Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Find the 5th order Taylor polynomial about a = r for sin x.

A: To find Taylor polynomial for given function

Q: S V9x² + 64

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Q: The particular solution y, of the differential equation y" + 4y' + 4y 3x2 + 1 is (1/8) (1-2x+6x^2) O…

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Q: } Consider the initial-value Question 2 ( problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. (a) Use…

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Q: The equation o=- in spherical coordinates represents sphere. Select one: True O False

A: Here, the given equation is: φ=π5

Q: Explain why the function f(x) = ez is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: Find the general solution of the given ODE x +1 y': y* +1 x? + r- - y? = x +4x + k Option 1 O Option…

A: integration

Q: Ssec10dE

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Q: Using appropriate trigonometric substitution, dx xV4 - x2 is transformed to 1 S csc 0 de cos e d0 2…

A: Topic = Integration

Q: Consider the differential equation (x- 1)y" + y' = 0. By using power series so- lution about the…

A: Please see the below picture for detailed solution.

Q: x-1 y = log, x+1

A: We know, ddxlog(x)=1x ddxu(x)v(x)=v(x)u'(x)-u(x)v'(x)v(x)2 log(ab)=log(a)-log(b) log(a)n=n*log(a)

Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is . Wha the…

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Q: Q3: Find gradient of the following function at given point 1) f(x, y) = y –x, (2,1) 2) g(x, y) = y –…

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Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

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Q: Differentiate y = -e24x + In(3x – 5). A. 72e24x – 120e24x + 3 y' %D Зх — 5 В. -72e24x + 120e24x + 3…

A: Given query is to find the derivative.

Q: A ladder 42 feet in length rests against a vertical wall of 36 feet in height. What is the measure…

A: Given query is to find the angle of elevation.

Q: Using appropriate trigonometric substitution, dx xV4 – x² is transformed to S sin 0 d0 sec 0 d0 2 2…

A: The detailed solution is given below Thank you

Q: Decide whether the given relation defines a function, and give the domain and range. Year (x) 2005…

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Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y = 0, a regular singular point is: X=4 x=2…

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