d²f , df_ (a) +5- - + 6f =0, f(0)=1, f(0) =- 4 dt? dt

Q: substitution to convert the integral to an integral of rational functions. Then use partial fraction...

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Q: ) Sketch the region enclosed by the given curves and find its area. y = -x² +4x, y=x² – 2x

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Q: Find a formula a, for the n-th term of the following sequence. Assume the series begins at n = 1. 1 ...

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Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where ...

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Q: If I represent the intensity of light which has penetrated water to a depth of h feet, then the rate...

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Q: Find y' : In(cos² 3x) = e*+y + sin¬1 y

A: Given that: ln(cos23x)=ex+y+sin-1y

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Q: Express the repeating decimal as a fraction. 0.451141414141... 0.451141414141...

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Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:  f...

Q: If the limit of f(x) is 5 and the limit of g(x) is 2 as x approaches a constant k, what is the limit...

A: If the limit of f(x) is 5 and the limit of g(x) is 2 as x approaches a constant k, what is the limit...

Q: Here is the graph of y = 2x – x². 2- 1- -5 -4 -3 2 3 4 y -1- -2- Find two possible functions f(x) an...

A: We need to find inverse function.

Q: Use the Quotient Rule to find the derivative of the function. f(x) = f'(x) =

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Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (If both values are the sa...

A: let the two numbers be x and y so  x×y=36sum=x+y since         xy=36⇒y=36x Substitute y value in sum...

Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate th...

A: Here, given that h-π4=12, hπ4=1 & ∫-11h(x)dx=2...(1)

Q: An+1 +00 to determine if the sequence { ne" }" is strictly increasing or strictly decreasing. An Use...

A: We will determine that given sequence is increasing or decreasing.Below find the solution in the ima...

Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where ...

A: topic - translation of a function

Q: Solve the Bernoulli Equation xyy' + y² = 2x

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Q: Error Analysis. Below is the solution (possibly, with errors) for the derivative of the given functi...

A: Given f(x)=3x-7 Formula ddx(x)=12x or ddx(xn)=nxn-1 Consider f(x)=3x-7=(3x-7)12 differentiating with...

Q: 4 - 3 + – Find the limit of f(x) = as x approaches o and as x approaches - ∞o. 9. 9 - X

A: Find the limit of the function .

Q: 1. Sketch the graph of y=2-x. 2. If fx) =x(*+2)(z-3), use interval notation to give all values of x ...

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Q: Error Analysis. Below is the solution (possibly, with errors) for the derivative of the given functi...

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Q: If the length of a certain rectangle were increased by 2 feet and the width decreased by 1 foot, the...

A: Let's find. 

Q: 4. (D² + 4D + 5)y = 50x + 13e 3x

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: An ice cream shop estimates that the revenue (in dollars) from the sale of x cones is given by R(x)=...

A: Given: - The revenue from the sale of x cones is given byR(x)=11000ln0.02x+1 To find: - The change i...

Q: ate the integral. (If the quantit 8. dx (x2 + 4)2

A: The given integral,                ∫-∞∞xx2+42dx

Q: What do I say?

A: Simplify :     csc(x)+cos2(x)sin(x)

Q: 1+ x)y = e¬=

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Q: Verify the following general solution, then solve. Find the particular solution to the differential ...

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

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Q: dy re: (e + e-")- = y² (separation of variables) da

A: Given that: (ex+e-x)dydx=y2

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

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Q: Consider the following. y = f(x) 4 8 (a) By reading values from the given graph of f, use five recta...

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the d...

A: We will solve by using alternative form of derivative as shown below 

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below 

Q: Find dy for y = (4x +2)2. dy = (Simplify your answer.)

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not evalua...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

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Q: A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never res...

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Q: Follow the curve sketching process for y = cos 2x + sin x on the interval 0, 2T using the following ...

A: The given function is: y=cos(2x)+sin(x) ;         x∈0, 2π

Q: (b) (x² + xy) = y² y = 1 when x = 2 dx dy (c) - y = e* sin(2x) y = 1 when x = 0 |

A: Given : (b)  x2+xy dydx=y2  ,         y = 1 when x = 2   which is y2=1 (c)   dydx-y= ex sin2x ,     ...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: The differential equation below models the temperature of a 94°C cup of coffee in an 18 C room, wher...

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Q: 3 sint dt O F(1. 25) + f(1. 75) + f(2. 25) + f(2. 75)] O f(1) + 4f(1. 5)+ 2f(2) + 4f(2. 5) + f(3)] f...

A: Solved below

Q: 24.) The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rate of ...

A: Area of the circle , A =πr2 ; where, 'r' is the radius.

Q: Which term best describes the mapping shown? a. relation b. function c. one to one function

A: Given query is to find mapping is a relation or function.

Q: What would the slope of the tangent line be at the point 3,3 on the folium of Descartes x^3+y^3=6xy ...

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Q: Find: WxtWy Wxy,xx Wyy W= I+xy-z²

A: GIVEN:- W=1+xy2-z2  To find:- Wx , Wy , Wxy , Wxx , Wyy , Wyx