a) Use Newton's method to estimate V5 with xo = 1. ( Find x1, x2 and x3 ) b) Find lim x→1 \x-1 using L'Hôpital's rule. Inx)

Q: 3-v49 B) Without using L'Hopital's rule, find: lim

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Q: Verify that L'Hopital's Rule applies and evaluate the limit.

A: The given question belonging to the calculus in which we have to find the limit of the given…

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: Prove that lim (Snt tn)z ş + t Note: s = lim Sn ţ = llm

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Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: Suppose that 2J of work are needed to stretch a spring from its natural length to a length 1m beyond…

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Q: 4) Use L'Hosp9tal's Rule to find the limits c) lim tanx)) メ→0 d) lim (ex + メ メ→ o

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Q: п! 1. Find lim via a Riemann Integral.

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Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: Evaluate the integral. S tan (2x) sec (2x) dx .5 Find the limit

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Q: The maximum value of y = sin x, 0 <= x <= 2p, isand occurs at x =__________ .

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Q: In (1 +) lim t1/2

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol 1-cos x sin²x (2) lim, o…

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- 9-3 (2) lim, tanr-sin…

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Q: Compute, from first principles, without using L'Hopital's rule eh – 1 lim = 1 h-0 h

A: (18) We have to evaluate the limh→0eh−1h. We know that the expansion of eh, which is given by…

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: 4. Use L'Hopital's rule to evaluate lim(1 – 2 sinh(r))ach(=).

A: 4) To evaluate: limx→0(1-2sinh(x))csch(x)  which is in 1∞ form.

Q: by L'Hopital's rule 1-cos(x) lim x2

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Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: Find the limits [ sin(3t) lim Li+ In(sin(3t)) j+tln(3t) k sin(t) In(tan(t)) t+0

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

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Q: What is the length of the arc y = (2/3)(x2+1)3/2 over the interval [3,6]?

A: We need to compute the length of the arc of the given curve over the interval [3,6]

Q: Iff is bounded and integrable in the interval [a, b], f(x) cos nx dx=0. show that lim

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Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

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Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: by L'Hopital's rule 3 sin 0 lim

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Q: use taylors formula to find the cubic approximation to f(x,y)=sin(6x+y) near the origin

A: Given Function,fx, y = sin 6x + y

Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

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Q: 3 (e) lim (1 x2

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Q: Express the limit lim,, +00 Ei-1 8i2 as a definite integral.

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Q: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(12r) lim

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Q: I* cos z lim 1³+2

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: 1- cos 3x lim &r

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Q: Evaluate lim wing sin2x +7x²-2x Wir 'Hopi L'Hopital's rule,

A: Consider the given expression. limx→0sin2x+7x2−2xx2x+12 Simplify the denominator.…

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.