4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1, given y = 3e** - + 8 In 5x. dx Give the answer correct to 3 significant figures.

Q: Sketch and use a double integral to find the area of the region R bounded by the lines: y = 0, y = x…

A: A detailed solution is given below.

Q: d太 2.

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Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

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Q: Find the general solution of ydy/dx =2/(3x2). a. y?/2 = -2x/3 + C O b. y/2=-2/3x + C O c. y/2 = 2/3x…

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Q: 5. Suppose that f(n) satisfies the equation 5. f(m + n) = f(m) + f(n) – 2f(mn) for all integer m,n…

A: The objective of the question is computing the value of f(n).

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Q: What is the volume of the region R = ((x. y, z) e R'1 sxs 3:2 sy S 4:3 sz5 5)? %3D Select one: O…

A: Volume of the region R is given by volume=∫13∫24∫35dzdydx

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Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

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Q: S tan5 x dx O 1/4 sec^2 x(sec^2 x - 1) - In Icosx |+ C 1/4 (sec^4 x - sec^2 x -In Icosx |)+ C O 1/4…

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Q: +00 dx II. Evaluate the improper integral x(In x)²

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Q: Find the function f(x) such that f''(x) = x + cos(x), f(0) = 1, and f'(0) = 2.

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Q: 5. sin x sin 4x dx c

A: We have to find integration value for the given function

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A: We can solve as follows

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Q: The dimensIons of awater tank are 13 cm, 10 cm and 70cm. If it is half-filled with water, cal-…

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Q: dx Vx²+2x+5

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Q: The Characteristic impedance is R+jwL V G+jwC Z. 6.74x10°+j22.1056 0.29x 10 6+j6.28x8.7x10

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Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: II. Matching Type: Match the definite integral in column A with its value in column B. Letters only.…

A: 11. ∫022x-3dx12. ∫-11x3+2xdx13. ∫03x2-2dx

Q: _12. What is the maximum directional derivative Daf of the function f(x,y,z) = x – y² + z² at the…

A: Let's find.

Q: For what values of a and b is the following function continuous at every x? - 10 XS-3 f(x) = < ax-b…

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Q: Compute the determinant of 11. 0260 0 0 3 7 8 00 4 Answer: enter number

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Q: 9) Local Linear Approximation a) Find the local linear approximation of g(x)= x° at x, = | b) Use…

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Q: cos (x) tan (x) dæ

A: I have stated the used formulas in the solution

Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

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Q: 2.S Ver eax dx Sve

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Q: V4. 4-x? Si S dy dx using polar Evaluate 2x-x2 Coordinates.

A: Let's find.

Q: cos x Given: tan x dx. Using trigonometric transformation , the integral in terms of u is sin x Cos4…

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Q: x arcsec x dx ? xdx A. x Arcsec x - 25- ... B. ** Arcsec x -- V-1 xdx xdx C. x Arcsec x + 25- xdx D.…

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Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

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Q: 2 Evaluate V4-x² dy dx using polar 2x-x2 Coordinates.

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Q: In polar coordinate system, which of the following does not refer to the point (3, pi/6)?    A. (3,…

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Q: 5. Let ƒ be a function satisfying the following properties: lim f(r) = 2 continuous on R \ {0} •…

A: a. Here, we have  limx→0-fx=-∞, which means the function has a vertical asymptote x=0; limx→+∞fx=0…

Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: 3. 2 What is the value of the integral 7xyz dxdydz ? 0, Select one: O 133/4 O 135/4 O 137/4 O 139/4…

A: To evaluate: ∫23∫12∫017xyz2dxdydz Let I = ∫23∫12∫017xyz2dxdydz First integrate with respect to x and…

Q: dx ex sin2 (e

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Q: 3 Find the arc length of the astroid: x = cos t, y = sinº t, 0 <t < 2T

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Q: Find the general (real-valued) solution of the following differential equations. If an initial…

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Q: Find the point on the line y = 5x + 2 that is closest to the origin. (x, y) = Need Help? Read It…

A: Let's find.

Q: 2. sin° (x) cos° (x) dx

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Q: Consider the function y = x^3 + 2^2 − 3x a) Sketch the graph of function. b) Find the instantaneous…

A: This question can be solved using the concept of graphs and derivatives.

Q: Find the limit or explain why the limit does not exist: x2 + 3x lim sin x Note: x is measured in…

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Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: (x Using a suitable trigonometric substitution, the resulting integral in terms of V9x²+4 Consider e…

A: Given problem:-

Q: 2. |=xp(x)JLOS Then find the value of the integral: pune f(0)=| Sketch, on a sheet of work paper, an…

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Q: Question 3 of 10 0/5 !! Incorrect. Use the following theorem to evaluate the integral/ le - 4|dx.…

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