[1/(2+x)]-(1/2). Find lim X-0 4 O 2 4 O -2

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

A:

Q: - «) lim (2 – ez x→0

A:

Q: 4 ex lim X 4 + 3e*

A: Given,              limx→∞4-ex4+3ex

Q: Solve the following by definition only: lim (4x - 5) = 7 as x approaches 3.

A:

Q: 1-cos x 9. lim x00 x2

A:

Q: Find lim x→-∞ ex + 1° (а) — оо (b) ∞ (c) 0 1 (d) 2 Does not exist and has no infinite behavior

A:

Q: Find lim(2 – x)tan(r2/2)

A:

Q: lim [r – In(4x + 7)] x→+0

A: To find the limit

Q: Q. 1. Evaluate the following -x* +3x +5x –18 a) lim 5x – 2x-0.5 Vx² +15 –4 b) lim x-1

A: We have to calculate the limit

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

A:

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

Q: 1S 章テ(メ) H+3x寸hen lim トーつ0

A: the objective is to find the derivative of the given function by using definition of derivative

Q: Q4: A) solve: 1+xsin 1) lim- y0 1+xcos sin 2) lim -2m 20-4

A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

Q: lim In(r) - 0t

A: Consider the given limit

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A: In general the right limit of the function  at a point gives the value of the the function as the…

Q: 32. lim x + x - 2 x2 - 1 2,

A:

Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

A:

Q: Find lim x→3- x2 – 9 for o, -inf for -o, and DNE

A:

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: Find the indicated if it exists: lim x to 8;  2x2+3x+1 divided by x4 - x2

A: To find the limit if exists

Q: - 2 lim c. x→o Sin(x)

A: It is given that X approaching 0 from the left, X<0. Therefore, Sin(x)<0. Therefore, the…

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: (금 1 Evaluate L = lim T→2 + x² – 5x + 6 -

A:

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: x2 + 8x + 15 if x 2. Find lim f(x). x-2+

A:

Q: if f(5) = 4, f'(5) = 7, then lim of (f(x²+1) -4)/(x²-4) = ?? when x goes to 2

A: Please see the answer below.

Q: Q1: limx-→n tan(x) is X-T 1

A: Given, limx→ πtanxx-π

Q: If 1(x) = 8x+9 find lim t(x). 10x+6' X+00

A: The given function is tx=8x+910x+6.

Q: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

A:

Q: lim x yields to 1  x-1/(square root of 4x +5)-3

A: As the given limit is not legible, the limit is computed in 2 cases. Obtain the limit as follows.

Q: If 4- 3x sg(x) s4 cos x for all x, find lim g(x).

A:

Q: Based on the previous item, what is x + 2 lim x→1+ x – 1.

A:

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: Find the following: x+/3 + 9x/5 (2х — 1)1/2 — 3 - i. Lim- x-0 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

A: a)

Q: V3r-1 7. lim X- sin? x-cos(2x)

A:

Q: |x² +1 if x 0 x→0

A:

Q: Q1) Find lim Bx+4-4cos²x+tanx x-0 4sin2x 10x2+125-5 Q2) Find lim x-0 3x2

A:

Q: lim h-->inf   10/ (h^2+100)

A:

Q: 7- x2 if x 2 Iff (x) find lim f (x). I→-1+ |

A:

Q: 1 Ask for the answer to lim x (1 – e * ).

A:

Q: Q4:Evaluate 1) lim (1-1) x-0 \sin x

A:

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: Q27. The value of lim x-0 (1+x)5-e5x+sin x² x2 is? →

A:

Q: 5) lim f(x) x--2

A:

Q: 5. Show that lim –nx² e dx = 0.

A:

Q: 399. [T] lim e(x - 1) x-1 x-1

A:

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: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.