3. Evaluate the following integrals. For each integral, briefly explain what method you are using and how you decided to use that method. (a) √ √ 2²³ ln (x) dx (b) sec¹(x) tan² (x) dx

Q: If f(x) = lim (1+x)(1+x²) (1 + x² ) (1 + x² ).......((1+x) where [x] < 1, then - 618 1 (B) 3) (C)…

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Q: 37. If antiderivative of m+p is equal to - 8 X³ √₁+2x² (B) 5 which passes through (1, 2) is…

A: We need to choose correct option.

Q: Q4: Let y = √t and a) 2 b) 3 c) 4 t = x² then y(") = 0ifn= d)5 e) others

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Q: If 0 = 0 and R = 7√2, then F₂ = 2

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Q: 15. Find the inverse of matrix A. A = 38 26

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Q: Below is the graph of a polynomial function with real coefficients. All local extrema of the…

A: (a)The function is decreasing in the intervals: (-∞, 9),(-6, -3),(1, 5),(8,∞). (b) The function has…

Q: Identify the vertex of the parabola: y = -4(x - 2) 2 - 3. (2, 3) (-2, -3) (-2, 3) (2, -3)

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Q: Q/Find the Taylor Polynomials of orders 0,192 and 3 generated by fat F(x) = Sinx 29=0

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Q: Convert the polar equation r² = 2 cos (-20) to a Cartesian equation. (x² + y²)² = 2x²-2y² (x² + y²)²…

A: In this question, we want to convert the polar equation in Cartesian equation.

Q: dx x √16-x² dx

A: To find out the integration.

Q: (a) (i) Calculate (4 + 6i)². (ii) Hence, and without using a calculator, determine all solutions of…

A: the complex number ..

Q: Q2: The equation of the tangent line to the graph of y=t² and t = 4x² at t = 1 is (not that x is…

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Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

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Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

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Q: cos(x² + y²) = y² sinx² y² = ln(x² + y²)

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Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

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Q: Printegrating Factors (x² - Sin²y) dx + x sin zydy = o

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Q: For the function f(x) = -5x, find the difference quotient f(a+h)-f(a) = h f(a+h)-f(a) h

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Q: 2) The expression 321 x 320 x 319 x 318 can be simplified as nPr. The value of n + r =

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Q: Choose the values that are in the range of y = arctan x. Select all that apply. ооо оо 0 ElFlo kio…

A: We have to choose the values that are in range of arctanThe range of arctan x is -π2, π2

Q: h(x) = [(x − 3)√6x − x² + 9 sin¯¹ (x-³)] g(t)e-2t (1+e-2t)-1/2

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Q: Solve the initial value differential equation with initial values y(0)=2 and y'(0)=6 y" - 3y + 2y =6

A: We have to solve the given differential equation.

Q: A tire manufacturer estimates that the demand function for their radial tires will be given by P =…

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Q: 4. 2ydx + (x x³y³) dy = 0

A: Here we have to solve the given differential equation

Q: Evaluate the integral 9x² √x² + y² dzdy dx

A: Given problem:-

Q: Enclosed by x² + 4y² = 16

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Q: } L 1 (s? +1)(s? + 25)

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Q: Evaluate the integrals. a. b. [x√1-x² dx X x sin cos 3 -cos-dx

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Q: dx (4+x²)² √

A: Explained below

Q: 3. dy dx + y = 2xy²e²

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Q: 2. Find the Domain of the function: h (x) = 4x x (x² – 9)

A: Given function h(x)=4xx(x2-9)

Q: -10 5. Given the polynomial: 2x³ + 19x² + 32x - 21 A) List all of the possible rational roots: B)…

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Q: Determine the volume generated of the area bounded by y=√√x and y=-x rotated around x=5. 2 A 128/15…

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Q: MATHS HOME A 41. If f (x) = f[ta (A) 3-e^/4 4 J'a (B). tan((nx) +- dx & f(1) = 0, then f (e/4) is -…

A: I am attaching image so that you understand each and every step.

Q: Q2: The equation of the tangent line to the graph of y=r2 and t=4x² at t=1 is (not that x is…

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Q: x³dx √1+x² (A) / (1+x³)³/² + (C) &n[√x - √₁ + x² + c 31. If I = f- then I equals to - " (1+x³) ³/²…

A: Follow the procedure given below.

Q: √9-2³ x² + y² dy dr into a double integral in polar form. TITE f(x, y, z)dV, where f(x, y, z) = x²yz…

A: We can set up the triple integral.

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 1. Given the function f(x) = 20 √7-x find f (-9). "

A: The given function is: fx=207-x    ...1

Q: Write z₁ and 2₂ in polar form. (Express in radians. Let 0 ≤ 0 < 2π.) Z₁ = √3+1, Z₂ = 1 + √√√3i Z1 =…

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Q: 1 Determine the volume generated of the area bounded by y=√√x and y=-x rotated around y=3. 2 A 16/3…

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Q: Use the theorems to evaluate the limit. 1 lim x → ∞ x2 ||

A: We have to evaluate the limit.

Q: 3. Worldwide annual sales of smartphones in 2013-2017 were projected to be a 9--10p+4,360 million…

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Q: es { [ (x² + 5) } 1_7²_

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Q: Find the directional derivative of f(x,y)=sqrt(x²+y²) at P(4,- 3) in the direction of μ=[8,-15].

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Q: provide a step by step solution to the following DE (2x+3)y' = y + (2x+3)1/2 when x=-1 and y=0

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Q: Reverse the order of the integration dy dx sin x

A: W need to find integral.

Q: Evaluate dy/dx using implicit differentiation.

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Q: 5) The number of 3 - digit numbers with repeats, that are multiples of 5 and less than 600 that can…

A: Permutation is used

Q: 2. Evaluate x sin xdr using integration by parts.

A: