Find a limit equal to (x2 – 8)dx. 3

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

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Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

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

A: We know that, ∫lnxdx=xlnx-x+C…

Q: Express (3*) dx as the limit of a sum. 1

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Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: Find the limit of sin Ø/Ø as approaches 0°. * 00 1 -1 ООО

A: Using formula.

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: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

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

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Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: Find for the following function. dx 5 cos x y= 6-7 cos x dx

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Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: use the chain rule to find dy/dx for the followingy=tan(2x-x^3)

A: Formula used:

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: dy Cos(3x) + (In x)

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: Find upper and lower bounds for

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Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

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

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

Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

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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: Find the indefinite integral. ∫arctan x dx

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Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

Q: 5 一=A+hxsl-x dy=?

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Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

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Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: 14x(e^(1/x))−14x limit x approaches infinity using lhospitals rule

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Q: x dx using Sim | size 0.3 is

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Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Find oy for dx2

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Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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Q: Evaluate the definite integral.

A: ∫012arccosx1-x2 dx Consider, ∫arccosx1-x2 dx Now put, arccosx=t⇒-11-x2=dtdx⇒11-x2 dx=-dt Therefore,…

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: Find the indefinite integral ∫ [arctan(x/2)] / (4 + x2) dx

A: ∫arctanx24+x2dx Now put, arctanx2=t⇒11+x22·12=dtdx⇒11+x24·12=dtdx⇒44+x2·12=dtdx⇒24+x2=dtdx⇒14+x2…

Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

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

A: The given probability distribution function is,

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.