2COS X-I Sin x, Yna1 = 2cosxy, – Yn-1+ n21 and 0

Q: cosh 1+j T 2 * T sin 1-j- 2

A:

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

A:

Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: Give a combinatorial proof of the identity (2)=3(") + ³(²) 3(3).

A: The combination formula is defined as (nr)=n!r!(n−r)! Therefore…

Q: 19. (For students who have studied calculus) Use mathemati- cal induction, the product rule from…

A:

Q: What is the coefficient ot x" in (x+3) '9? What is the coethicient et x? in the expanson ot lx +2) 4…

A: Binomial theorem expantion

Q: Q4/ A- If p (A) =0.4, p(B) 0.2 and p (An B) 0.1 determine the following properties P(A'), P (A U B),…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: x² – 4 Evaluate: A =Vx2-4+ sec-스)+C ⑥ -Vx2-4+2 sec-스)+C =V x2 – 4 – 2 sec + C (D =2Vx2-4+ sec-1스)+C…

A:

Q: Evaluate L{e-2t sinh 3t} s - 2 s2 + 4s – 5 3 2 a) s² + 4s – 5 b) c) s2 + 4s – 5 d) s2 + 4s – 5 a 3.

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Q: dx_ -In x – 2 |x+2 X - + C x² – 4 - 4 Select one: O True O False

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Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

A:

Q: the second image is not loading?

A: Here we will use the ratio test for convergence of series

Q: x2 dx is (ax2+4)(x2+9)

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Q: Evaluate [²√₁-Pa dx °ex√1_(ex)2 ofile कस 0 √i-(ex)

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Q: Evaluate ex sin x dx. A - ex (cos x + sin x) + C В e* (cos x + sin x) + C C) -ex (sin x - cos x) + C…

A: We will find out the required solution.

Q: Sz sin?m-10 cos2n-10 = – B(m,n) В (т,п)

A:

Q: d.x 81+9a4

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Q: Show that cosh x> 1 + x² for all x.

A: comparison

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.