Assignment: L'Hôpital's Rule. Include supporting mathematical statements within a grammatically cor- rect exposition. Compute the following limit using exponentials and logarithms with lim (3x)tan(5z)

Q: Find the limits

A: We divide the numerator and denominator by x.

Q: 6. Give an example to show that not every function is one-to-one. Explain your reasoning.

A: The objective of the question is give an example which state that every function is not one-to-one.

Q: X -2 Prove: lim e

A: The limit of a function is the value that function appears to achieve when reaching a certain value.…

Q: Find the limit.

A:

Q: Find the limit. x!000 lim x→+0 et

A:

Q: Calculate lim where an 2". an+1 n00 an

A:

Q: Each graph represents f"(x) (not the original function) Find the x-coordinates of all inflection…

A: We have to find the x- coordinates of Inflection point.

Q: + 75 3-4x Evaluate lim x-4 1 -4x-6 + Enter an exact answer. Provide your answer below: 13

A:

Q: 15. When given a limit to evaluate, explain, using examples, how you know which method you choose to…

A: Evaluating limits is a process of finding the value of a function as the input variable approaches a…

Q: Use the graph of f shown in the figure below. y 1아 5- -10 -5 10 5 -10아 Find f-1(-3).

A:

Q: Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous…

A: Explanation given below...

Q: Evaluate each limit graphically. 1) lim *→-1 - 48 -6 कर x+1 ix-xf(x) nitaoni -4 -2 2 K

A: The existence of limit at To find:-

Q: Let e be a positive number. Explain how to shift the graph of y = f(x) upward, downward, left, or…

A: Given: y=f(x)'c'  be the positive real numberTo shift the graph of y=f(x),  upward, downward,left,…

Q: Determine the infinite limit. x + 10 lim X-9- X + 9 Step 1 As x approaches -9 from the left, the…

A:

Q: Topic :Limits   Give a value that is close to 3 but not equal to 3.

A: According to the given information, it is required to determine the value that is close to 3 but not…

Q: = lim r++m et + ex et - e-x

A:

Q: 1. lim 32x-1 X→2 2. Find the limit. 2. lim 2e*+2 – 3 X→-2

A: We have to solve the limit problem

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.