e? – 1 – z lim 2 z-0

Q: 4. Let 1 4- t ift 2 Find the value of c so that lim B (t) exists. t-2

A:

Q: 3. EVALUATE AS AN INFINITE SEMES: 0.5 a. e dx lim x- In (1 + x) b.

A: We know that, ex=1+x1!+x22!+x33!+x44!+.........................=∑n=0∞xnn! and…

Q: 2. Evaluate the following: Va2-x² So Sa* x² ydydx а. xsin x b. lim-2cos x+e

A:

Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: Evaluate I (n +) lim as n → 0 Vn[ (n + 1)

A: We have to evaluate limn+32n⋅n+1 as n→∞ that is limn→∞n+32n⋅n+1 We know that n=n−1! Hence,…

Q: B. Evaluate the following limits. 1+x-e* 2. lim x-0 1-cos x Csc t 4. lim (cos t)ª t→0 csc e

A:

Q: fr'e* for 1 <x<3' for 0<x<1 If (x)= {e then limf(x) is A. O В. 1 С. е D. e E. nonexistent

A: The given function is defined for the interval [0,1) and (1,3].

Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

A:

Q: Which one of the following is equal to lim 2 sec x – 2cos x :? The limit does not exist. a. О. 0.5…

A:

Q: Which of the following expres zy 0 = .lim(z,9)¬(0,0) F+ y²

A: Let us substitute: y = mx Then we get, Limit as (x, y) tends to (0, 0), [(xy)/(x2 + y2)] = Limit as…

Q: 2.14 Show anx" + ... a12 + ao lim n an bn .. provided that b, # 0.

A:

Q: that Find the implhes positive N such h > N ) lim E = 0.01 h -a 00

A:

Q: to evaluate the limit. 3 1 v 78. lim x→ x Jo im In(1 + e') di | In(1 + e') dt 2

A: Answer is  1/2 Explanation is given below

Q: 3 of 20 Select the best answer. (2e + 1)ª lim z+00 (tan(x))- O DNE

A: We have to find the limit.

Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

A:

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

A:

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Question 12 Find the limit lim e2x+2h _ e 2x h-0 h O 2e* et

A:

Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: In(z+ y) (a) lim (a,) (0,) z-y

A:

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: 10.2.29 Because 0.5 1. e 3+(1/3"-1)

A:

Q: Let y' = -(1- y/k) where k > 0. If y(0) > k/2 and y(0) + k then lim,0 y(t) = k A. true B. false

A:

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: How can I find A, k, and C with the following information? L(t)=-(A/k)e^(-kt)+c Lim as t approaches…

A: Given function,

Q: 1+ V5 Let s1 = 1 and for n > 1, let sn+1 = Vsn +1. Show that lim s, = 2 n00

A:

Q: Which of the following is not true? 4dx 4dx A S.. lim √x(x+6) c √x(x+6) 5 dx dx So 25-x² B = lim…

A: We have to find out the option

Q: cos x In(x – a) | 40. lim In(e* – e) X→a+ -

A: Use L hospital's rule when of the form type of inderminate 00.

Q: 3) see the attached file 3-the limit of this function cos x-(2 cos 2x -1) lim equal to 1-cos x A)2…

A: Given function is ; cosx - (2cos2x - 1) /(1-cosx) at x tendes to zero we find the limit .

Q: 1. Show that for all f e L'(R) lim

A: To show: limδ→1∫f(x)-fxδdx=0 Concept used: ∫fxdx=Fx+c Chain rule: ∫fxadx=1aFx+c

Q: e -e lim is z0 In(1+ 2x)

A: Given limit:

Q: tan z lim is Select one: a. e b. 0 с. 1 d. -1

A: Given limx→01xtan(x)

Q: lim, »00(e² + x)!/z =? O a. 0 O b.1 O. Limit does not exist. O d. e O e. 00

A:

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

A:

Q: 8. lim In(+h)–1 A. 0 B. - C. 1 e D. e E. Does not exist

A: To solve the limit.

Q: 1) Answer the following: 1. Find: lim-5-25 x-5 2. Find x2 + y? = 9xy dx 3. Find y': y = 5 sin3x

A:

Q: TY +1 lim (1,)→(0,0) 2 + y² OA.-1 =? B. Does not exist O C.0 OD. 1

A: By converting two variable limit into one variable limit, we calculate the required limit.

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can…

A: Given that functions g(t) and h(t) are defined for all values of t and g (0) = h (0) = 0.

Q: Evaluate the limit: limo* [cos(3x)]= O e-3 03 e 01 ◄ Previous

A: To evaluate the limit.

Q: 'e in + = "T 2n Find lim a

A:

Q: In(x), 5 s x s 16 f(x) A = lim n- o 2 i = 1

A:

Q: e 2t In (1+7) t lim t→+o t1/2

A: Let L is the value of given Integral.

Q: Find lim e dt 0. 1 1/e

A: We find out limit of given function. See 2nd step.

Q: a) Show that for any & > 0 and S₂ = ₁X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n n→∞

A: We will use Chebychev's inequality to find the limit of the given probability.

Q: (x + x)T 3 - x) dx = lim n- 0o n If where a, B and y are positive integers, then a + B +y = зо 20 16…

A: Given, ∫-21x2+xdx Here, a=-2 and b=1 We know that, ∆x=b-an=1--2n=3n and xi=a+i∆x

Q: In (x + h) – In x (c) lim h→0

A: To find the limits  Here variable is h , so assume x as constant. 0/0 form , so use L-Hospital's…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.