Let C be the shortest path that connects n to ni and I = [, (sinhz + 1)dz. Then O I=-sinh n+ n(i-1) |=-1-cosh i+ n(i-1) O I=-sinh + i(1-i) None of these O I=-1-cosh n+ n(1-i) O l=0

Q: 29. Show that sin x rif0<1 <2m.

A: Given a function sin x and 0&lt;x&lt;2π To show sin x&lt;x for all values of x such that…

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Q: 5. Solve tan² (2x) = 1 in the interval [0, 2π).

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Q: if 2E2, f(2)= 12₁² find @if 20 then f/2) not exists Oif 2=0 then find f(z)

A: Given that fz=z2, then find  1) If z≠0, then f'z not exits. 2) If z=0,then find f'z.

Q: A- L [ Sin2t + cos2+] ² 2 B 32 3-2 [37-² + cost's *] 3 2

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Q: sec x=1/5 on [0,2pie)

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Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: find the valups of 'a'and b' that nakes 8x2+ 8 x2+ +5 X L-1 K(x)== 6 x= -1 con tinuous at x =-| x 7-…

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Q: xy" - (4x + 1)y + (4x + 2)y = 0,

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Q: Let Express the value of in terms of I. pn/12 0 tan ¹2 (2x) sec (2x) dx I = p/12 10 S tan ¹0 (2x)…

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Q: If sin\theta =-(1)/(2) and 3\pi <\theta <(7\pi )/(2), then

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Q: d'y If 4x2 + y = 40 then evaluate when = 3 and y = 2. (Answer accurate to two decimal places.)

A: Topic = Derivative

Q: (3) Prove that n=2²°² is a square. 2K+1 where K = 1 $ (n)

A: This follows from the definition of euler Phi function

Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: prove the following relationships. Note that x(z) = ] [x(+)]. 1. ] [ a^² XLE)] = x ( ² / ) 2. ] […

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Q: Which of the following is not equal to the derivative ofy = (cos(x) – sin(æ))= A 2 (sin? (x) – cos²…

A: The given function is y=cos x-sin x2

Q: 110. π/3 -π/3 /sec²x - 1dx

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Q: find the first and Second derivatives of the equation fon = Sin [√sex+x³²e² 3 SX X. C tanx J-ex

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Q: Convos) 32 =0 oR What are the 5 vouts of -32? 5 So lve Z°+ Findall the poots of the fimectin: f(2)=…

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Q: sin20 6. J 1-cos 0

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Q: s2 L-1 (s² + a²)² 1 [sin at + at cos at] 2a

A: If the Laplace transform of a function f(t) be F(s), I, e L{f(t) }=F(s) then f(t) is called an…

Q: d6 1 2-₁ {-101 = ds6(s-7)2-64, 13. If L-1 6₁)} = atbect senh(8t), the value of (a.c) is:

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find -2s3 + 9s² – 8s + 18 -1 s (s2 + 4) (s + 1) (3-5e+3 sin 2t ) (4 - 5e' + 2 sin 3t) (1-3e+3 sin…

A:

Q: Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C.…

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Q: Solve the following ODE * (y sin x + xy cos x) dx + (x sin x+ 1) dy =0 1 Add file

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Q: • To find sn, we raise $₁ to the power Sn ||*)/2-1/ 1/n 2-1/2) 2(n+1)/2 |sn|1/n Sn = 1/2 n

A: The given step is

Q: dy If y = 9sin x then dx (a) (cosx) 9sin x (b) (In 9)9 sin x (c) 9sin x (d) (In 9)(cosx) 9sin x

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: List all intervals for which there are possible unique solutions (t-5)x''-ln(t)y'-y=et

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Q: 419 *Ocosec™* 6d8 is equal to

A: Given integral is ∫sec4/9θ cosec14/9θ dθ

Q: {b_n}={3^n/n!}

A: We first expand the summation sign

Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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Q: What is the domain of r(t) = e'i + tij+ cos(t + 8)k? (Use symbolic notation and fractions where…

A: We have to find the domain of the given function r(t).

Q: The velocity of a particle moving back and forth on a number line is ds = 3 sin(3t) dt for all…

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Q: 71. Use Figure 4 to prove V1- 12 d /1 – x2 + sinx FIGURE 4

A: Let A be a point on a circle of unit radius(r=1) with origin as its center, such that: Calculate…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.