Evaluate and approximate f(x) dx of the functions in Table 3. ,2 4 1/(1 + x*) V1+ x² | sin(y) e

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

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Q: The linear approximation at x 0 to sin(2x) is A + Bx

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Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: Compute d/dx  sin-1 (x/x+1)

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Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: 2- Find dy/dx for y = In(tan(2x2))

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Q: Given: f(x) = / (2 – 4t) sin() - dt %3D tan(2r) 17 – cos(2nt) Find the equation of the line tangent…

A: The tangent is a straight line to a curve that touches the curve at exactly one point. The point…

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: 8. y = In(2e-t sin t)

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Q: 1. Calculate the Integral sin x cos x dx

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

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

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: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: 5. y = l 1- co s x 1+co s x

A: We have to find out dy/dx for given y

Q: 5 一=A+hxsl-x dy=?

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Q: Let e 2* = 2 find dy dx at x = 1

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Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

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Q: find dy/dx. g(x) = cos x/sin2 x

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Q: 3) Find dy given 3xy = In x. dx

A: Given  3xy=lnx To find dydx   implicit differentiation is used Both sides have to be differentiated…

Q: ) Given the function f(x) derivative f"(1) with h, h/2 and h/4. 5. e Vx cos (Tx), approximate the…

A: Given function is  For this answer, we choose  We have  (up to 4 decimal place accuracy) We also…

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: 1- find dy/dx as a function of x. y = sec (tan x)

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

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Q: 1) Find dy/dx if : y In (tan¬ x)

A: Given : y = lntan-1x

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: 3 cos x Evaluate | dx by using substit ution method. (1+sin x)“

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Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: 1. [z x cosx dx 2. x sin 4x dx 3. xedx 4. x Inx dx

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