Find the limit x-1 lim x>I* Vx +2

Q: evaluate the limit lim x→1+        (ln(x)) / ( ln(x − 1))

A: Given:

Q: Evaluate the limit tan x lim x →0 2x

A:

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: Find the one-sided limit (if it exists).

A: We will find the limit numerically  Let, x y -0.1 -5.0000025 -0.01 -50 -0.001 -500…

Q: Evaluate the limit. limx→ 0+ tan-1(1/x)

A:

Q: Find the limit. -5x cos(x) lim

A:

Q: Find the limit limx→0ax−1x.

A: Given, The limit is,

Q: Evaluate the limit: lim (x - ln x)* x→0+

A:

Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

Q: Find the limit. x!000 lim x→+0 et

A:

Q: Find the one-sided limit

A: Given: limx→2+ xx-2 To Find: To evaluate the given limit.

Q: Find the limit. lim sech(x) X -0

A: To find limit: limx→-∞sechx Solution: We know that sechx=2ex+e-x Therefore,…

Q: Evaluate the limit using L'Hospital's rule: x13* lim x→0 13* – 1 -

A:

Q: Find the limit. lim x+v-1 (x, y)- Vx+y-1

A: The given limit is of 0/0 form. In this type of limit problems, we try to remove 0 from the…

Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

A:

Q: Find the limit. lim_(x→∞)xsin(1/2)

A:

Q: Find the limit. (x²-7) (6- cos x) lim

A: Given,           limx→0x2-76-cosx

Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: Determine the infinite limit. X 1 lim x4+ X - 4 -CO

A: We will plug x=4^+ in the expression first. We got 0 in denominator. So lets check by plugging…

Q: Find the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R.

A: We find the pointwise limit  lim_(n→∞)(ex/n/n) for x ∈ R.

Q: lim x" x→0+

A:

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: V4+x-2 lim

A:

Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

A:

Q: Calculate the limit algebraically. lim (x + Jx)

A:

Q: Find the limits lim tan-x X-

A: Solution: consider the given limit function; limx→-∞tan-1x Let  tan-1x = y⇒tan y = x when x → -∞…

Q: ■ Find the limit.

A: Given: limx→∞ x2 - x4   To find: Value of the limit.

Q: find the limit. lim x→∞ e-x (sin x)

A:

Q: 4) Determine the limit. lim 1 f(x), where f(x): X + 10 X-- 10-

A: Given, f(x)= 1/(x+10)

Q: Find the indicated limit algebraically. Show complete solution. 2x -x-3 1. lim x--1 2. lim () x+1…

A: Solution: Consider the given limit function is limx→-12x2-x-3x+1 We can factorized numerator and…

Q: Find the limit limx→1x11−x.

A: Given that limx→1(x11-x)We need to find the value of limit

Q: Find the limit. lim x-0

A:

Q: lim x3 In(x) X→0+ to

A:

Q: Evaluate the limit. 5 sin(x) – 5x lim x3

A:

Q: Find the limit L. 2x2 + 8x + 6 lim X--3 x + 3 L =

A: Factorise 2x2+8x+6 2x2+8x+6=2x2+6x+2x+6                     =2x(x+3)+2(x+3)…

Q: Find the limit. limx 0 √(x2 + 4)

A:

Q: Find the limits lim x→1- sin-1x

A:

Q: Find the specified limit fCx)=(x+2,x>-1 lim, fa)=3 ×マー

A:

Q: Find the limit. lim e^(-2x) x-->∞

A: To find the limit of e^(-2x) as x tends to infinity.Check whether the L Hopital’s rule applies.

Q: Find the limit, if it exists.

A: First of all, use the limits property and apply the limits on numerator and denominator.

Q: Find the limit. lim etan x→(3t/2)+ х

A:

Q: Find the limit. lim sech(x)

A: Given:limx→∞ sechx

Q: Find the limit

A:

Q: Find the limit, if it exists. Vx6 - 1 lim x5 - 1 X--0

A:

Q: ■ Find the limit.

A: To evaluate the limit: limx→2π-x cscx Solution: We know that limx→2π-sinx=0- Now, evaluating the…

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

A:

Q: Find the limit, if it exists. lim x - -0

A:

Q: Calculate the limit limx→∞(1+6x)x.

A: limx→∞ (1+6x)x   = limx→∞ (x+6x2) = limx →∞ x + limx → ∞ 6x2 = ddx x + ddx 6x2 = ddxx + 6× ddx ×…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.