Q5: Differentiate the following: a. f (x) = In(3x + 2)5 b.y = (2x* + 1)tanx c. f(x) = etan(2x)

Q: The lowest point on the graph of y = cos x, 0sxs21, occurs when x=

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: 07) If y = tant ,x= tan²t at t =. Find by using Chain Rule

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Q: Show that y = tanh x is an odd function.

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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: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: 8. Find the principal value of Arc tanh(1 + j2)

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Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: Find the root of the function using Fixed-point Iteration. f (x) - x cos (x) - x?

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Q: If f(x) = sinh³ x %3D the en f'(x) = ||

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Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

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Q: Find y double prime using implicit differentiation5x^3+4y^3=1

A: We have given,

Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…

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Q: (5tan28 etan 28 sec² 2 Bd B

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Q: How many periods of the function y = sin x are there between -10T <0<6T ?

A: Given that y=sinxTo find : number of periods in interval  -10π≤x≤6πSolution : period of sinx is 2πin…

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

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Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: y" + 2y' = sin 2x ||

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Q: ∞ sin2x dx (x²+1)²

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Q: Find the absolute extremum f(x)=sinx    (30,120)

A: Given function is Differentiating with respect to x, we get Firstly, we find critical points of…

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: 8. Find the Laplacian of Ø = xy²z³

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Q: Find the derivatives of the functions in Exercis

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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

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Q: 4 The range of y =sinx for 7SXS is 2 0syso 4 <ys0 sys1 ys 4 -1sys,

A: We are given a function y(x) = 4/5 sin(x) and we need to find the range of y(x) when π ≤ x ⩽3π2 (…

Q: For what x-value (approximately) does the function f(x) = sin(x) – x reach height -2? (Use a = 2 as…

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Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Which formula gives the x-coordinates of the maximum values for y = cos(x)?

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Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

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Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: tanh" (cose 3x

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Q: Use Secant method with p0 =1, p2 = 1.2 to find the root of f(x)= Inx - cosx that is accurate to…

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Q: lim sin (xt3) dt X 5

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.