Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polynomial for the function in sigma notation. 9 cos(T2)

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A: Given: dydt=t2y-y+t2-1   We know that; ∫1ax+bdx=1alnax+b+C And The Power rule: ∫xndx=xn+1n+1+C ; n≠-...

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Q: Find the derivative of the following functions using the limit definition.  1. z =7y2- 11/y 2. f(z...

A: From limit definition of derivative we know, f'(z)=limh→0f(z+h)-f(z)hand f''(z)=limh→0f'(z+h)-f'(z)h

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A: ∫01/2arcsin(x) dxIntgerate by parts ∫fg=fg=∫f'gf=arcsin(x), g'=1f'=11-x2,g=x=xarcsin(x)-∫x1-x2dxSubs...

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Q: cot 2x J Tcot22x – 15

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Q: Find the derivative of the function. S(2) = VE - 8E f (x) =

A: topic - derivative of a function

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

Q: let f(x)=5x^3-9x^2-3,x ≥ 1.5. Find the value of (df^-1)/(dx) at the point x=f1 =f(3)

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A: 1/(x-6) >= 1/5 solve this inequality. 

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Q: Prove that n° + 2n is divisible by 3 for all n E N. Prove by induction that if p is any real number ...

A: Note:- according to the company policy we can attempt only one question so please upload the next qu...

Q: 2. Given: a1 16, а4 1024 Find: az =? а. 12 b. 18 с. 36 d. 64

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Q: 2. (x + 2) dæ: (x + 3) sin y cos y dy In(a + 3) sin y %3D + C ans. x -

A: (x+2) dx = (x+3) sin y cos y dyUsing the method of variable separable;x+2x+3 dx = sin y cos y dy   ∫...

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Q: Find the derivative of the following function using the limit definition: z =7y2- 11/x

A: We need to find derivative.

Q: Consider the following sequence: 7" {an} 3n2 n=1 An+1 to show that the given sequence {an} is strict...

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Q: Evaluate the integral x cot x² sin(in |sin x²l) dx.

A: LetI=∫ xcotx2sinlnsinx2dxSubstitute u=lnsinx2Differentiate du=1sinx2ddxsinx2du=1sinx2cos(x2)ddxx2du=...

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Q: FIII in the yellow box to complete the truth table of "p v (q →r) V q->r "p v (q →r) r 5.

A: Concepts:   ~ p is oppostite of p.p=T then, ~p =Fp=F then, ~p =T   Implication Truth table:   Disju...

Q: S(z) = 64 –3 V/

A: f(x) =x964-x3We can rewrite the function as;f(x) = x9  164-x3f(x)=x9 (1641-x364)a=164,  r=x364   (Ge...

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Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: Which of the following is true about horizontal asymptotes? OAll rational functions have at least on...

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Q: Obtain the general and particular solution 3. xcos²ydx + tanydy = 0

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Q: nd the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about = zo and then find the nth Taylor po...

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Q: Write the first five terms of the sequence: +00 {Vn² + 10n – n}-1 n=1 Determine whether the sequence...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 (-1)k+1 k8/...

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 00 5+ 2"...

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Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

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Q: Use the Laplace transform to solve the initial value problem below: b) y" + 3y' + 2 y = f (t) Where ...

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Q: A. F(x) = (1+æ) sin(x)+ B. F(x) = (1+ sin(x))(1+ c. F(x) = (1+ x)(1+ sin( %3D %3D %3D

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Q: create a graph with labels of a function that  satisfies:  have one point where f(x)=-3, at least o...

A: Question- create a graph with labels of a function that satisfies:    have one point where f(x)=-3, ...

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

A: The given series is: ∑k=0∞56k+3=563+564+565+566+... which is a geometric series with the first term ...

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Q: 1. Use the definition of a geometric series to rewrite the following series

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