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Q: (d):e-2! (i) : e¯' sin 2t e): cos(5) (j): e“ cost 3t

A: (d) Given:        e-2t     =Le-2t   use Laplace transform table : Leat=1s-a       here a=-2         ...

Q: Find y' and y". (x – y)3 = x – xy + 1

A: Topic :- Derivative 

Q: 3. Solve the equation: x(2x +7)=4.

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Q: NONEXACT DE DIFFERENTIAL EQUATION (2x?y - 2y2 + 2xy)dx (x² - 2y)dy = 0 2. +

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Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate 4mi^2...

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Q: a? -1 x² +2x+- ;x 0 Let f(x) =- Find all possible real values of a such that f(x)possesses the small...

A: The given function is: f(x)=x2+2x+a2-1a4-5 ;          x<0x+2                     ;x>0

Q: Let x 2. -3x, f(x) = 1, 3x, Find the indicated one-sided limits of f, and determine the continuity ...

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of integ...

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Q: If possible, let be rational. a Then, there exist positive co - primes a andb such that- /2 b

A: Given:         Let us assume 12 is rational.            12=ab ...1       Here, a and b are two co-pr...

Q: The function s(t) describes the motion of a particle along a line. s(t) = t2 − 18t + 26 Find ...

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Q: h(x) = 1 – x – x2 (a) Express h in standard form. h(x) = %3D

A: We will solve the problem 

Q: Find the quadratic function y = ax² + bx + c whose graph passes through the given points. (1,2), (– ...

A: Here given that y=ax2+bx+c...(1) which passes through (1,2), (-1,-8), (-3,6) To find a,b, and c for ...

Q: Find the absolute maximum and absolute minimum values of f on the given interval f(x) = 5 + 54x - 2x...

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Q: If f'(a) exists, then lim f(x) A. must exist, but there is not enough information to determine its v...

A: Here, given that f'(a) exists. To determine limx→af(x).    

Q: Compute the directional derivative of the following function at the given point P in the direction o...

A: Given:- f(x, y) = e-x-y , p(ln(3), ln(2)) , <1, 2>  To find:- Compute the directional derivati...

Q: The profit P from selling x units of a product is given by P = 550x – 0.2x2. The sales are increasin...

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Q: Graph the function: 2x-1 for x<1 f(x)= -2x-1 for x>1

A: `Given f(x)=  2x-1   for x&lt;1 f(x)=   -2x-1  for x&gt;1

Q: Solve the quadratic equation 9x -15x +6 = 0 by the method of completing the square.

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Q: Suppose that the number of bacteria in a culture at time t is given by N = 3000( 26 + te ). (a) Find...

A: Here, the given function is: N=300026+te-t10 where N is a number of bacteria in time t.

Q: The region bounded by the graph of y = x²VIn x and the x-axis on the interval [1, e] is revolved abo...

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Q: Consider the function f, which is attached. Check the following values to see if f is continuous. U...

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Q: Determine the open intervals on which the graph of the function is concave upward or concave downwar...

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Q: Q: If possible, let E be rational.Then, a there exist positive co - primes a andb such that 12 b

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Q: Solve DE (1+e")dx+e ay3D0 1

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 3s 4, s 8 -

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Q: QUESTION 4 4.1 A motor company manufacture and sell cars and motorbikes. The cost of manufacturing x...

A: As per the guidelines, I have provided solutions for the 1st two part as they are inter related. Ple...

Q: Compute the derivative of the given function in two different ways. 6t + 1 f(t) t + 5 g.f' – f · g' ...

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Q: a) f(x) =x³ + 9

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Q: Find the limit. X400 lim x→+o er %3D i

A: find limx→+∞x400ex=?

Q: The function y = f' (x) is graphed here. Our task is to sketch one of its antiderivative functions, ...

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Q: f(x) = x4 − 2x2 − 24 (a) Write the polynomial as the product of factors that are irreducible over th...

A: The given polynomial is  f(x)=x4-2x2-24

Q: An airplane flying at an altitude of 5 kilometers passes directly over a radar antenna. When the air...

A: Given:- An airplane flying at an altitude of 5 kilometers passes directly over a radar antenna. When...

Q: 1+xcosx Evaluate: dx 2.2 sin x x(1-x'e**)

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Q: 9. Evaluate lim In sin 2 5х 10. Evaluate lim sin 2 3

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Q: The period of a pendulum is given by the equation shown below, where L is the length of the pendulum...

A: Let's find. 

Q: Find the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your ans...

A: Given: f(x) = x² - 2/(2x² - 18)

Q: volume

A: Please refer to the image below

Q: Convert 105% to two other ways of expressing part of a whole…

A: Given percentage,  105 %

Q: x2 + 9x + 18 Let f(x) 5x + 15 (a) f'(4) = (b) f''(4) [NOTE: There are two ways to do this problem. T...

A: NOTE: Refresh your page if you can't see any equations. . see, if we use the quotient rule to find ...

Q: Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions.

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Q: 1 Let y = -. Find dy and Ay at x = 7 with dx = Ax = – 1. Enter the exact answers. dy = Ay =

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Q: ? Let f(x) = { a? - 1 +2x + aʻ-5 x0 Find all possiblereal values of a such that f(x) possesses the s...

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Q: f = (-0.17) =

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Q: y = In(cot x). Find O A. cot x 1 O B.- sin x cosx |C. - csc². CSC OD. cotx O E. sin x cos x

A: Given; y = ln(cotx)

Q: Coffee is poured from a kettle into a cup at a temperature of 95°C . After one minute of cooling in ...

A: For the solution of the problem follow the next steps.

Q: ? Let f(x) = { a? - 1 +2x + aʻ-5 x0 Find all possiblereal values of a such that f(x) possesses the s...

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Q: Given f(x) = -4 f(2)-f(1) 2х-1 find x e (1, 2) such that f' (x) = 3x-4' 2-1

A: Given, f(x)=2x-13x-4

Q: he axis of symmetry is parallel to the y-axis and the parabola passes through the points (0,0), (3,0...

A: Given that: Axis of symmetry parallel to y-axis and parabola passes through (0, 0), (3, 0) and (-1, ...

Q: Compute the derivative: d (24 da I=3 The derivative is:

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Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

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