Q1: A. Find the general solution of the following Initial Value Problem (IVP): y-2y-3y=e²t 8. Find a unit vector that points in the same direction as q=1+3j +9k

Q: √√3 L dx 1+x²

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: Let A= de ghi Assume that det(A)=-11, compute the following. NOTE: Enter all values exactly. (a) (b)…

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Q: a. b. Evaluate the following integrals 2 dx cos²x√4 tan x- tan² x I [ sin(√a)da dx

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Q: the argument of the Complex number: Z= ¹+√ √B-j

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Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: Find 넥 L -TS (s+1)e- s² + 4s + 4

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Q: Let 7' (t) = Find a parametric equation of the line tangent to r(t) at the point (59, 0, - 2.303)…

A: Follow the procedure given below.

Q: Q4. f(x)=5 and 1(x)de=8 dx = 5 and f(x) dx = 8 then f(x)dx a) -3 b) -13 c) 13 d) 3 dx is given by

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny [the Low +¹Y2 ex+y dxdy 0

A: See the details solution in below

Q: Q4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

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Q: Q1- Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x)

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Q: Evaluate using Partial Fraction Decomposition: x² (x+1)²(x-1) -dx

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Q: A car is moving with uniform acceleration. it covers 200 m in 2 sec and 220 m in next 4 sec. the…

A: A detailed solution is given below.

Q: f(x csc² 2x − x cos 2x)dx

A: Given problem:-  ∫(x csc2(2x) -x cos(2x)) dx

Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: 9+xn 5n n=0 An empty set since the series diverges Find the domain of ƒ(x) = Select one: O (-1,1) O…

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Q: ax x(x² - 1)

A: The given integral,       ∫dxxx2-1

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

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Q: solution = Give the ODE : general x" + 3x² - 4x of the following

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Q: Question 5. Limits at Infinity; Horizontal Asymptotes For the function f whose graph is given below,…

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Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

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Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

Q: If f(x) = 5³x then f'(x) = 5.A 5h 3 In S O 3x(5³-1) 5³ (In 125) 3(5²)

A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

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Q: A movie poster is to contain 0.48 square meters of colored print. The margins on each side are 2.54…

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Q: Consider the region bounded by y = ex+1, y = 1, and y-axis. 1.5 0.5 -1.5 -0.5 0 Which of the…

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Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2eycosy + = C 2. 3…

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Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

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Q: Use the transformations to graph the given function. Show all translations on each transformation.…

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Q: By using double integrals, find the surface area of plane + y² -+z=c that lies inside a a the…

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Q: Find the coordinates of the vertices of the polygon after the indicated translation to a new…

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Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

A: This question can be solved using the concept of maxima and minima.

Q: Solve the following. x³-x²-√2x limx→21 x2-11x+18

A: To evaluate the given limit, first, we multiply the numerator and denominator of the given function…

Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: 1. Given the function f(x)=2-4x+ +$. Please find the intervals of increase or decrease, absolute…

A: Given problem:-

Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: Please help me with this homework. I am working on (x-5)^2 , (y-3)^2 and (z-1)^2 but said my answer…

A: We need to find (x-5)2 , (y-3)2 and (z-1)2

Q: Calculate √√3 8 2 1/√3 1 + x² dx

A: Given ∫13381+x2 dxTo evaluate the integral:

Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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Q: f(x csc² 6x - x cos 6x)dx

A: Given, ∫(x csc2 6x-x cos 6x)dx

Q: Find a power series representation for the function x f(x)= 9+x² and determine the radius of…

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Q: Let r(t) = Find fr(e) de (don't include the +C) fF(t)dt = < [

A: Given,  r→(t)=-4t4-3,-4e3t,-2sin(-t) ∫r→(t) dt =∫-4t4-3dt,∫-4e3tdt,∫-2 sin-tdt

Q: 2) for evdxdy

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Q: During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s…

A: According to the company policy we are supposed to answer only first three sub parts and rest of the…

Q: The Cartesian coordinates of a point is (4, - 4√3). This point in polar coordinates can be…

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Q: (x²+2) dx x+2

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Q: Integral Calculus

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Q: What is the domain of the function f(x)= |x|? 0 (-∞,∞0) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

A: We need to find domain of given function.

Q: e2-1 Evaluate: limx→0 2x²+x 01 O ∞ 00 O None of the choices 02

A: The given limit is: limx→0e2x-12x2+x   As we know that; The Chain Rule: fgx'=f'gx·g'x