-π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

Q: 25 √x²√5 − x²dx = − x(5 - x²)(5 − 2x²)+² Arcsin(x)+c

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: ƒ dx = f(+ g(x)) dx, then A + f g(x) dx is equal to x³+x A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

A: Given that,

Q: Do as indicated. 1 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the…

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Q: A B Consider the integral f sin ¹x dx. If we let u = sin-¹x and dv= dx, the integral can be written…

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Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: Explain why you think the sequence 7 converges to a finite number or (-8)"-1 diverges. If the…

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: trigonometric substitution, what is f √x²-9 x3 sec ¹(-₁)-² + C √x²_9 2x² sec 6 ¹(-)- √x²_9 2.x² + C…

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Q: Find T(t) and N(t) at the given point. T(0)=(1,1,1) N(0) = (0, 2, 1) x = e cost, y = et sint, z=e¹;…

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Q: Question 1 sec42x Find -dx tanº2x -=(corº2x) ( 11 12 tan62x cot22x- - (cort2x) A - 1/1 (0 (A) B…

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Q: Using partial fraction in evaluating A 6-2x B 2x-6 © - ²7/ 1/1/2(2x + 1) = 7/7/2 Ⓒ - 1/2…

A: Solution of given question is written in below steps.

Q: 15x²x343x - 19 The integral (x + 1)²(x² - 6x +13) can be rewritten as Slax [ax² + bx² + c + (mx +…

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Q: Find the average value of the function over the given interval and all values of x in the interval…

A: Let's find.

Q: B C D N Given: √-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms…

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Q: Integration of Algebraic Functions By trigonometric Substitution dx 6. S x²√4-x² dx 7. S- √81+x² X…

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Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

Q: Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by…

A: This question can be solved using the concept of dot product and cross product of two vectors and…

Q: x²+x+1 rb dx g(x) Sa 2x²+2+73+x dx =[Af (x) - B ln(g(x)] + D fod, and if A =,B<0, then dx = P x+2'…

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Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: Using trigonometric substitution, what is sec-1 (-) √x²-9 6x² + C sec (1) √x²-9 6x² + C sec-¹ √x²-9…

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Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. (x - 1+1/2/3 1. lim x-1 2x²…

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Q: Calculate the derivative. f(x) = (6e* - 7x²) (x³ + 1) (Use symbolic notation and fractions where…

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√x-1 1. lim 4. lim 5 3x - 4 2.…

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Q: Find the radius of convergence, R, of the series. n Σ -(x + 8)n 30 n=1 R= Find the interval, I, of…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: The equation 2k² - 3k 10 = 0 has solutions of the form k N± √D M (A) Solve this equation and find…

A: The given equation,    2k2-3k-10=0

Q: 3x^2+y^2=28 3(x-1)^2+y^2=19

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Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: 2 (tan²x + 1)√sin2x.dx= (tan², 0

A: Find your answer below

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Question 7 10 -8 -6 -4 -2 8 10 -2- -4 -6 -8 -10 Write an equation for the graph, where y depends on…

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Q: 25 1. ƒ x²√5 − x²dx = − ²x(5 − x²) (5 − 2x²) + ²5 Arcsin (5x) + C 2009

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Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: Find F'(x). +2 x+² (4t + 1)dt a. F(x) = b. F(x) = ft³dt sinx c. F(x)=√t dt d. F(x) = f sin t² dt e.…

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Q: Use the formula (t) k(t): ||r' (t) x r"(t)|| = 13 ||r' (t)||³ r(t) = e¹²ti + e-tj = to find k(t).

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Q: dx secx+1

A: Given ∫dxsecx+1We do half angle substitution:=∫1tan2(x2)+11-tan2(x2)+1dxSubstitute…

Q: +x+1 2x² +2+x³+x dx = [Aƒ'(x) − B ln(g(x)] + D, and if A=B<0, then f x+2 -2x + +5In(x + 2) + C 2 x²…

A: Solution of the problem as follows

Q: Solve 4t² +8t+4= 0 by using the square root method. Hint: complete the square first! Enter each…

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Q: x = 48 cos(t),

A: answer is in next step

Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraint.…

A: we have to find the point (x, y)

Q: (A) = and B = . Find the vector projection of A D onto 2A - BO O O none of the above

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Given point(1,-2,3) Then the equation of the line passing through 1,-2,3 is…

Q: 2-1 dy y2-2y-1

A: Explained below

Q: Explain why you think the sequence converges to a finite number or n+1 diverges. If the sequence…

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Q: Use the formula к(t) : = ||r′(t) × r"(t)|| ||r' (t)||³ 9t r(t) = e⁹ti + e-tj to find k(t).

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Q: d Calculate dt [ri(t) · r₂(t)] and [ri(t) × r₂(t)] first by differentiating . dt the product…

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Q: The IBP formula fudv-uv-fvdu can also be written as fudv + [vdu = uv Which of the following…

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Q: Find the horizontal asymptote of f(x) = y = 5x + 2x³ +3 5x³x2-4

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Q: II. Find d Do not simplify your answers. 1. log,(√2x² + y) + tan(z* — x") = sin−¹(x² − 1) + ½

A: This question can be solved using the concept of differentiation of implicit function.