lim cot(z) %3D - 10 -1 0 3 0

Q: lim = 0 || x→00 X X 00

A: To show: limx→∞1x2=0 Solution: Given limit is, limx→∞1x2 As,x→∞,⇒x2→∞And,1x2→0 (As,1∞→0)⇒limx→∞1x2=0

Q: lim f(r). エ→2+

A:

Q: sin(a+x)-sin x 3. limx-0

A: limx→0sin(a+x)-sinxx

Q: Find the one-sided limit

A: limx→12-x secπ x Now secπ x tends to ∞ as x tends to 12 from the left side.

Q: @lim Jerz - J V3 @ lim Vat6 - 2 x3-2 X+2 Olim V5-x -2

A:

Q: lim I→-3+ x +3 O a O b 1 - 00 O d

A:

Q: VE -1 lim エ→1 エー1 = 1/2

A:

Q: lim Example 21. x → 0 Jx + a - Va: |

A: see below the answer and calculation

Q: lim f(1) = 1, lim f(z) = – 00, I -2 f(- 2) = 1

A: Please see the below picture for detailed solution.

Q: lim x->infinity  6e10x

A: Given: -

Q: m cot(6x) / csc(6x) = ? x-> 0

A: limx→0cot(6x)csc(6x)∵cot x = cos(x)sin(x)   , csc(x) = 1sin (x)

Q: lim x → 0

A: →When limit is of the form 00 or ∞∞ then we use L'Hospitals Rule  →In L'Hospitals Rule , take…

Q: Find the limits

A: The given expression is limx,y→3,4x2+y2-1

Q: Find the limit

A:

Q: lim (x,y)-(0,0) x-y+2√x-2√√y √x - √y a) √2 b) 0 c) 2 d) -√2

A:

Q: lim (cot2 x x2 3/2 2/3 -2/3

A:

Q: Lim (x+1)ot* cot x x - 0

A:

Q: lim (x,y)(2,-3) x 2.

A: We simply put limit here.

Q: lim (x,y) (0,0) 2x3 + xy² + y x2 + 7y2

A:

Q: lim -5 -1 X→2 lim (s – 1)(s + 7) -2 s→-7

A:

Q: Evaluate the limit.

A: Given: limx→-∞x2-x3e2x for evaluating given limit, we substitute x=-h, after that simplify it and…

Q: Find the limits

A:

Q: lim x csc 25x x csc

A:

Q: lim 2 Sin

A:

Q: lim 1 2/x2 x→0 3

A: It is in the form of 1^infinity. So i have used the rule for that particular case

Q: Integral of the 10th question

A: Given: limt→∞ ∫0t(tan-1 x)2dxt2+1 =limt→∞ 1t2+1…

Q: lim x + vx - Vx = |

A: Given : To find the limit of the given functionlimx→+∞ x+x-x=?

Q: lim x 0 e*

A: To find the value.

Q: x4 - y4 25. lim (x,y)→(0,0) x ² + y2

A:

Q: secy-1 Lim seczy-1 a) as y → 0 b) as y – → 1/2

A:

Q: lim x cscʻx

A:

Q: lim esec x(7/2)+ sec x

A: We will substitute x= h + pi/2

Q: lim 2 -V1-x find Value. 3 +x

A: We need to evaluate the following limit limx→02-1-x3+x

Q: lim infinity x square root 3x

A: Here we can see from the help of graph of square root of x.

Q: secy-1 Lim sec2y-1 a) as y → 0 b) as y → T/2

A: To determine the value of the limit limy→0secy-1sec2y-1, apply L'Hopital's rule.…

Q: sin (n x) ii lim( + π) x-1 x-1

A:

Q: Find the limits

A: Consider the given function, limx→∞x2+25-x2-1 rationalize the function,…

Q: lim x approaches infinity x1/x

A:

Q: lim (x,y)-(0,0) x-y+2√x-2√√y √x - √y

A:

Q: lim X->I 2 2 tan ()

A:

Q: six decimal places). x2-3x lim -3 2-9 х3-2.5,-29,-2.95, -2.99,-2.999,—2.9999; -3.5, –3.1, –3.05,…

A:

Q: lim 6x2.cot x.csc 2x

A:

Q: Calealate: C lim (y-x )(1+n)

A: The objective is to solve the limit limx,y→0,0y-x1+xy+x1+y Let, y=mx Then…

Q: lim h->0 sqrt(1+h)-(1/h)

A: Given function

Q: (а) lim h 1- e-h sin x (b) lim

A: a). limh→01-e-hh=limh→01-1ehh=limh→0eh-1h·eh=limh→0eh-1h·limh→01eh=1·1e0…

Q: lim (x, y) → (4, -2) x2y + xy2 x? – y2

A: The given expression of the limit is: lim(x,y)→(4,-2)x2y+xy2x2-y2

Q: lim f (x) %3D X-2

A: Given that : Graph of the function :

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.