an exponential function y f(x). (2,8.64) (1,7.2)

Q: xdy +(y– xy+2)dx = 0

A: The given differential equation is; xdx+(y-xy+2)dy=0

Q: Consider the following system on (-1,∞0) × (–1, 0), 2y 2x 1+ Y 1+x 1. Find all the equilibrium point...

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Q: Question 6 Find the derivative of the function y = 8ln(cos 2x)+ 5tan? (3x) Write the value of y' (0)...

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. cos(n...

A: Given query is to find series converges or diverges.

Q: The volume of a sphere is expanding where r = 2t. What is the rate of change in volume with respect...

A: First substitute the value of r=2t in volume ,and then differentiate it for finding the rate of chan...

Q: Write the trigonometric expression in terms of sine and cosine, and then simplify. cos(u) cot(u) + s...

A: Question- Write the trigonometric expression in terms of sine and cosine,and then simplify:  Cos(u) ...

Q: Give the domain of t(x) = V-1- x in interval notation. (-0,1) Hint: Remember that, when we are worki...

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Q: 4. Assume y(x) = eaª cosBx is one of the solutions of the DE у3) — Зу" + 7у — 5у %3D 0. - - Then α +...

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Q: Given the curve in rectangular coordinates x² + 4x + y? – 8y = – 11 Find the parametric equations gi...

A: parametric equation of circle

Q: JA 1 J 40. f(x) x'+3x + 7

A: Given query is to find the interval where function is increasing and decreasing.

Q: d'y Find dz? of the function given implicitly: 6xy + 7e = 7e.

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Q: Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a fun...

A: Solution is written in below steps.

Q: The shaded region, R, is bounded by the graph of y = x² and y = 4, as shown. a. Find the area of R. ...

A: 1.Area of the region R:A=2∫04x dyA=2∫04 y dyA=2 [y3232]04A=43[y32]04A=43(8)A=323 square units

Q: Assume y(x) eaa cosBx is one of the solutions of the DE y(3) – 3y" + 7y' – 5y = 0. - Then α β (A) 3 ...

A: The given question can be solved as shown in step2.

Q: y = /x+ /x

A: We will use algebraic techniques to find the derivative.

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t  

Q: 32. In y = 2y² - x; (2, 1)

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Q: An+1 -to determine if the sequence is strictly increasing or strictly decreasing. Use the ratio 1 5n...

A:   The given series is n5n+7n=1∞ Let the sequence  an=n5n+7. Now, an+1=n+15n+1+7.  

Q: Q2) Show that y = 35 x* – 30 x² + 3 satisfies ( 1– x² )y" – 2xy' + 20y = 0 %3D

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Q: ollowing functions: b) y = (cos x)Vx*

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Q: For positive constants c and k, the Monod growth curve describes the growth of a population, P, as a...

A: Given: P=crk+r Recall: uv=u'v-v'uv2    

Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =...

Q: Use sigma notation to write the Taylor series about x = xo for the function. 10 In x; xo = 1 k =

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Q: Find the derivative of the function. (t) = (9t + 14)2/3 6 f '(t) = (9t + ly)1 3

A: Given that        f(t) = (9t + 14)2/3 Here we have to find f'(t) .

Q: 03) Evaluate the following integrals: A) y = sec(tan-1x). tan³(tan-1x) 1+x2 dx

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Q: Use the difference a+1 – an to show that the given sequence {a, } strictly increasing or strictly de...

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Q: #1 only

A: Topic:- differential equations

Q: 5. For the parametric curve z = 1- tť, y =t – ť°,t € R find: (a) the points where the tangent line i...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x0 and then find the nth Taylo...

A: This question is based on Taylor series.

Q: At noon, ship A is 140 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing no...

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Q: B Resort Number of rooms A Total 114 134 181 285 714 a) Determine the standard divisor. (Type an int...

A: Since only part a is visible, henc answering part a. Given query is to find the the standard divisor...

Q: Find the derivative of the function. f(t) = 8r2/3 - 4t/3 + 8 f '(t)=

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Q: The standard form of the first order linear differential equation x'y'+ry +2=0is

A: The standard form of a first-order linear differential equation is:

Q: Find the derivative of y with respect to x. 1/9x²-1 + sec -13x, x> y= cot %3D

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Q: A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r ...

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Q: Solve the given equation. (Enter your ans 2 cos?(0) – cos(0) – 1 = 0

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Q: 5 In(x); xo = 1

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Q: on 3 of 9 cies empt History Correct. y method to determine whet

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Q: Find the derivative of the function without using the Quotient Rule. y

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Q: 7. 4. A firm's marginal cost and revenue functions are given by MC- 12e + 16a + 20 MR = 100 -29 a. R...

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Q: Q1) Evaluate the following integral using By Parts Method: х.In(x3 + x) dx

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = –4, f'(0) = 13, f"(0) = 14,...

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Q: Let S be the region enclosed by the graphs of y = 2x and y = 2x² for [0,1]. What is the volume of th...

A: We have to find the volume of the solid.

Q: Sue wants to build an enclosed area behind her house for her pets. One wall of the enclosed area wil...

A: area of rectangle 

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increas...

A: Given :Radius of thr ripple increasing by 2 feet per secondCircumference = 2πr

Q: graph the folloring f un Ction %3D

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Q: Find the derivative of the function. g(x) = 2(3 - 8x)

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Σ k! k = 1 Identify a...

A: topic- sequence and series  

Q: Write (1-az2-bz)/(1+bz) as a product of linear factors.

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Q: Determine whether the series converges or diverges. In(k) Σ k k = 1 converges O diverges

A: