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

Q: (D² — 4)y = 8e²x — 12 - -

A: Given; D2-4y=8e2x-12 So, the auxiliary equation is; m2-4=0

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: y = (2x²+1) 3x²+1 2

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Q: ♫/² sin ( cos() sin (²) dx (Consider initially the first 2 terms)

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Q: value(s) of x where the tangent line is horizontal for the function f(x) = x²(x – 5)³. tiple answers…

A: Topic:- application of derivatives

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

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

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

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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: The region R enclosed by the curves y=x and y=x^2 is rotated about the x-axis. Find the volume of…

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Q: S 1 x√x²-4x-1 =dx = -Arcsin x √5

A: Topic:- integration

Q: √a²-x² -dx √a²-x² X --Arcsin (). + c

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

A: The given limit,     limx→-∞x2-x-x2+x

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

A: Explained below

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

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Q: Question 12 Determine the equation of the vertical asymptote and the equation of the slant…

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Q: olve the nonlinear inequality using the Number Line method and Interval Notation. Make sure to test…

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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: d d [ri(t) r₂(t)] and[r₁(t) × r₂(t)] first by differentiatin dt Calculate the product directly and…

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Q: Find T(t) and N(t) at the given point. x = T(0) N(0) = = = e cost, yet sint, z = e; t = 0

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Q: e²+2y + sech T = cot y + log2 (tanh x)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: II. Find Do not simplify your answers. dy da tan ¹(cosh x) 2. y= (sin² x) (sechar)sec z [use…

A: Given data÷

Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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Q: How many times will you perform integration by parts to evaluate sin (Inx) dx? A 4 (B 2 1 3

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Q: Write an equation for a function that has a graph with the given characteristics. The shape of y =…

A: We can find the correct answer as below.

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: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

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Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x + 13) Ax + B What is the value of dx ? ax²+bx+c 31 -…

A: Given integral ∫15x2-x3-43x-19(x+1)2(x2-6x+13)

Q: Question 8 Using trigonometric substitution, what is f √x²_9 x3 A sec (-²) – + C √x²-9 6x² B √x²_9…

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Q: Solving z² + 14-7-0 by completing the square method produces an equation of the form (z + h)² = k.…

A: Given,              x2+14x-7=0

Q: √√√x²-9 Consider x³ what is the integral form in terms of? 1 A Scos²e de B Scos²e de Ⓒ-S sin²e de C)…

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Q: Use linear approximation or differentials (but not both) to estimate: cube root of 7.98 Is your…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: d d Calculateri(t) r2(t)] and 77[r1(t) × r²(t)] first by differentiating the product directly and…

A: We need to find derivative.

Q: Compute the area bounded by the curves x=2y² and x=4+y²

A: Area bounded by two curves x=f(y) and x=g(y) is given by, A=∫abf(y)-g(y)dy ,a,b are the points of…

Q: Find the area of region bounded by the graphs of the equations. a. X b. y = x + sin x y + 3 2 1+ -R…

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Q: Consider using the method of partial fractions to solve dx x²+x+1 2x²+2+x³+x - dx = [Aƒ (x) − B…

A: Given problem:-

Q: Find the radius of convergence, R, of the series. (-7) xn n√n n = 1 R= Find the interval, I, of…

A: The given series,        ∑n=1∞-7nnnxn

Q: Find the absolute maximum and absolute minimum of the function f(x) = 3 sin (x) cos (x) over the…

A: Absolute maximum and absolute minimum on closed interval [a ,b] : 1.) Find critical points of f(x) .…

Q: In the following graph draw the vectors v = [0, 3, 1] and w = [0, 1, 4]. (a) Highlight the…

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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: Find a general solution of the system x'(t) = Ax(t) for the given matrix A. -20 -15 15 A = 8 7-5 -…

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Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: [sin³ (2) cos(4) dx

A: Follow the procedure given below.

Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: To evaluate S (In x)² -dx, apply integration by parts twice. For the second application of…

A: Follow the procedure given below.

Q: Calculate the difference quotient for f(x) = x + x¹ at a = 9. (Express numbers in exact form. Use…

A: Given query is to find the derivative and the tangent equation.

Q: dx tan x +sinx+1 Half-angle Substitution

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

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

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Q: 4. Evaluate the following sin(x)cos(2x)sin(3x) dx A. B. C. D. sin(3x) cos(3x) sin(2x) cos(2x)…

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