NUMERICAL DIFFERENTIATION Use the values of y (x) = cos r at r = {0, ) to estimate (a) y" () to order h (c) y () to order h? 16

Q: tangent equation at given value points. F(x+h)-f(x) Use f'(x) = lim h-0 b. w = g(z) = 1+ 4-z, (z,w)…

A: given function is w=g(z)=1+4-z find the equation of  the tangent at (3,2) find the differentiation…

Q: Determine the following limits analytically.

A: Given that : The limits is limh→0 sin(x+h) - sin xh , where x is a constant .       i

Q: Implicit differentiation Find dy/dx for the following implicit relations. y ln (x2 + y2) = 4

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Q: 1. y= sin (x² + 3x + 1)

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Q: 5. y = Arctan² (x³) '2х-1 6. y = Arccos 3x+1/

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Q: sinh (x) esin h-' (x) sin h- (x) Vx²+1 -esin h¯' (x) sin h Vx²–1

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Q: Using the differentiation with the first principle or the long method of differentiation, find for…

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Q: Separation of Variable (cos'x-sin x+ sin' xkx + sin x sin y(1- sin x)dy = 0

A: Separation of variables

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in…

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Q: Find the limit

A: We know that cos0=1  For x=0-, cosx will be less than 1.  So, |cosx-1|= -(cosx-1)= 1-cosx for x=0-…

Q: DERIVATIVE OF A TRANS FORM 2t Lte sen6t

A: Use Laplace Transform table:   Ltkft=-1kdkdskLft

Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

Q: y=sin-1(x/x^2-1)x=3^1/2 find the equation of the tangent line

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Q: How to avoid loss significant figures : (i) 1- cos(x), x is near 0. (ii) (v1+x² (ii) x - sin(x), x…

A: (i) Let,  f(x)=1-cos(x), x is near 0.  To avoid loss of significant figures,We can replace cos(x) by…

Q: Sin 2x- Cos 2.x Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: See the attachment

Q: Fourier series f(x)= x sinx 2 xe (7)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Derivatives of inverse hyperbolic functions Compute dy/dx for each function.a. y = tanh-1 3x…

A: we have to take the derivative of the inverse hyperbolic functions Compute dydx for each function.…

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

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Q: Applying the Second Derivative Test Find the critical points of f (x, y) = (x2 + y2)e-x and analyze…

A: We have to find the critical points off (x, y) = (x2 + y2)e-x and analyze them using the Second…

Q: (.0 < x < . Using the concept of Mean Value Theorem show that cos x <

A: To show: cosx&lt;sinxx2 ; 0&lt;x&lt;π2. Proof: Let fx=cosx-sinxx2. Mean value theorem: Suppose f(x)…

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, '2x-1 1. y = Arccos…

A: To find: The derivative of y=cos-12x-13x+1. Formula used: Chain rule of derivative: fgx'=f'gx·g'x…

Q: E. (DERIVATIVES OF TRIGONOMETRIC FUNCTIONS) 1. If f(x) = secx + 3 csc r, then 2. If g(x) = x² sinx -…

A: To find the derivatives of the following functions.1 fx=sec x+3 csc x2 gx=x2 sin x-3x cos x+5 sin x

Q: slope of the line tangent to the curve cos(5x-4y)-x(e^-x)=(-7pi/2)*(e^(-7pi/2))at the point…

A: To find the slope we need dy/dx We differentiate both sides of the given function with respect to x.…

Q: ,3 8. 4 cos (x) sin (y) = 1

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Q: f(x) = x sin x

A: Given data:     The given function is: f(x)=x sinx. STEP-1 The expression for the limit of the…

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 1. y = sin (x? + 3x +…

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Q: Inconclusive tests Show that the Second Derivative Test is inconclusive when applied to the…

A: To show second derivative test is inconclusive.

Q: 5. Interval 0 <x<n, function, f(x) = cos x.

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Q: Linear approximation Find the linear approximation to ƒ(x) = cosh x at a = ln 3 and then use it to…

A: Our Aim is to find the linear approximation to f(x) = cosh x at a= ln 3and then by carrying forward…

Q: integral using evaluate the substitution Sin(x) cos5lx) dx

A: Given,          ∫0π3sinxcos5xdx

Q: cos(x (*). cos(x + h) – cos x cos h – 1 sin h - - sin x · h COS x h h

A: Require to verify the identity cosx+h-cosxh=cosxcosh-1h-sinxsinhh

Q: Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

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Q: Inverse identity Show that cosh (cosh x) = |x| by using the formula cosht = In(t + Vr - 1) and…

A: Given : cosh-1(coshx)=x for all x   and  cosh-1t=ln (t+t2-1)    Claim :…

Q: 5. y = Arctan²(x³) 2х-1 6. y = Arccos 3x+1/

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Q: sin a Determine the derivative of sec x sec x cos z-sin z sec tan e sec2 a O 1 1-sin x sec2 x sec2 x…

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Q: 3. y = cot(x + 2) cosh(x + 2)

A: Given: y=cot(x+2) cosh(x+2)                                  Here, cosh(x+2) is hyperbolic function…

Q: Using "Numerical Differentiation (Central Finite Difference)" Problem Solving f(x) = 4e-2xsin(x2)…

A: 1. The product rule for differentiation states that ddx[f(x)·g(x)]=g(x)f'(x)+f(x)g'(x), where f(x)…

Q: 1 2. Find the derivative of y =V1 - x2 +arcsin x 2°

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Q: Consider the function on the interval (0, 27). sin(x) f(x) 4 + (cos(x))² (a) Find the open intervals…

A: Find out the intervals on which the function is increasing or decreasing and also find out the…

Q: (sinh4dx 11. cosh2x

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Using the rule of sign evaluate e - वय x (a- Differentiation under Integral 1 +1 e-9x) dx x x

A: Note: In the question it has to be ∫0∞e-xxa - 1x + 1xe-ax dx, otherwise the question will not be…

Q: sin(3x)-sin x - cot(2x)= cos(3x) - cos x

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Q: Linear approximation for the sine function Find the linear approximationto ƒ(x) = sin x at x = 0 and…

A: To findLinear approximation for the sine functionGivenƒ(x) = sin x at x = 0

Q: 4. у"- Зу' + 2у cos e*

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Q: 5. 2х + Зу\ %3 х2

A: Given :  2 x + 3 y 4 = x 2  Find :   implicit differentiation

Q: cos (x)+cos(x+x)= 0 = cosʻ (x)+cos(T+x)=0

A: cos2(x)+cos(π+x)=0 use trigonometric identity cos(π+x)=-cos(x) The equation becomes…

Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx…

A: On solving this we will get

Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

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Q: DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS 3.) y'of y = In x+1 by logarithmic…

A: Differentiation

Q: QI Find f'(x) for 1+ sec1(x) (x) = 1- csc-1(x) -csc (x) + sec (x) csc '(x) + sec '(x) V(x? - 1)(1-…

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