Suppose a E R, where a > 0, a # 1, what is[a"]? dx a" In(a) © xa²-1

Q: d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

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Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: -sinh(x) at x = 0 is dx21 Answer:

A: Derivative of the function

Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

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Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

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Q: Evaluate dx dy in y=cosh(in e") b. 3x sinh (In x') 3x² sinh(In e* ) d. 3x sinh (3x² ) с. a. 3x…

A: Given:     y = cosh ( ln ex^3 )

Q: Find

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Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: what is dy/dx?

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Q: / Find dy/dx of the following function y = 3tan-2*ln(sec(2x)

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: et Calculate the integral: dx (e – 4)(e* + 5) -

A: Given,            ∫exex-4ex+5dx

Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

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Q: Approximate 2x e 2 dx using three equal subintervals. - 1

A: To Approximate

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: find dy dx 15 In 4+ xe) 6

A: dlnax+bdx = a.1ax+b.

Q: Use Romberg's method to compute dx 1+x? correct to 4 decimal places by taking h= 0.5,0.25 and 0.125.

A: AS PER OUR GUIDELINE WE ARE SUPPOSED TO ANSWER ONLY ONE QUESTION. KINDLY REPOST OTHER QUESTION AS…

Q: Find e dx approximately using Simpsons rule with n 10.

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Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

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Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: FIND DY/DX OF THE FOLLOWING 6. y=sec'Inx

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Q: dy dr

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Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

A: let f(x)=17ex2 differentiating four times to get fiv(x) because the fourth derivative will be non…

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Show /x^ In х dx xn+1 ((п + 1)In x — 1) (п+1)2

A:

Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: Jrin m In(cos m) dm

A:

Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: dy find the dx +Ince 义 9 = sin In Cl+e)

A: The given problem is solved below in detail.

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 1 dx is finite -1 X Select one: True False

A: True

Q: Find d when y = 3 In(In(In(x))) dy dx

A: Here we can find the derivative as below

Q: d y' of y= In(tanh2

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Q: Find de when y = In(1+ 5/æ) dx

A: The objective is to find derivative.

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In A + (In V) (Inx)2 2) y = tan (x*)

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Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: find the antiderivative of dx/sqrt(ex-1)

A: To find : The antiderivative of dxex-1 Solution The antiderivative can be evaluated as, ∫dxex-1 Put…

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: e2: S dx 1+ex

A: Given the integral ∫e2x1+ex dx u = 1+ex  ⇒ ex = u - 1 du = ex dx By substitution method, I=∫e2x1+ex…

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

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Q: Find dy for dx 6) In y = In xe*

A: Topic:- derivatives