1+iz : If w = Find the im age of z|<1. 1-iz

Q: 3/2 3. Estimate (3cos x)dx using five subintervals and right endpoints. Sketch the graph and shade…

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Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

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Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: 20. What is the value of SSy? (SHOW YOUR WORK)

A: For the given data ( 20 ) SSY = ?

Q: (c) cos lim (tan x)°os x x-(플)-

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Q: 4 In estimating | cos(3x)dx using Trapezoidal - 1 and Simpson's rule with n = 6, we can estimate the…

A: Error bound of Trapezoidal rule and Simpson rule for integrating f(x)dx in [a,b] is, ET…

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

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Q: The maximum value of y = sin x, 0 &lt;= x &lt;= 2p, isand occurs at x =__________ .

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Q: (7) coshx + sinh x = e* %3D

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Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: 1+3x – cosI 2.) lim tan x

A: limx-&gt;01+3x-cosxtanx When we plug in 0 for x then we get…

Q: 1- Cos(ux) lim x-)0

A: Given expression limx→01-cos4xx2 Recall the identity 1-cos2x=2sin2x limx→02sin22xx2

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: Approximate the length of the curve using n secant lines for n = 2; n = 4.y=ln x, 1&gt;=x&gt;=3

A: We have been given a curve y=lnx and we are supposed to approximate the length of this curve between…

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: 4 Test for homogeneity fx,y)- tanx- see'x - Osy

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Q: S x2tan (x³)dx

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Q: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: Find Critical Points and Extreme Values: f(θ) = 2 Sinθ + Cosθ        on [ -2π, 2π ]

A: Given         The critical point is where  f'θ=0              Here the interval is -2π,2π…

Q: Find an equation of the tangent line to y=10sin(x) at x=π / 6 (Use symbolic notation and fractions…

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Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

Q: ar is exam. pility that th

A: The probability of producing defective cars given car produced by factory 1 is, PDF1=0.02 The…

Q: limit x to infinity (1+sin(3/x))^x

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Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: on inteaurron (ii) Determine the general formula for V Pn.

A: Numerical analysis.

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: dr =ズ Sin )=s OP Type a a exact awser Using X as needed

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Q: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

A: Find the exact length from 1 to 2: y=((1/4)x^2)-(1/2)ln(x)

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: 1-2 c) dx

A: Evaluate the integral: ∫01e1-xdx. Simplify- ∫01e·e-xdx Apply ∫afx dx = a∫fx dx here a is constant.…

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Find all transition points for the interval [0, 2]. 3 y = 3x + sin(3x) %3D

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Q: 11 Show that Simpson's rule withn=2 (so there are 2n = 4 subintervals) gives the exact value of (2x…

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Q: 1 - cosh x lim x→0+ ln(x² + 1)

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Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: