for each positive number X Evaluate lim

Q: Evaluate the lim x→0 X

A:

Q: If 3 lim f(x) =- then lim [4f(x)]=6 True False

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: f(x) – 7 10 , evaluate lim X→1 If lim X→1 X- 1

A:

Q: If х-+5 lim f(x) = 15, find lim ( 2x – x² /f(x)+ 1 х—5

A:

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

A: We first factor the denominator

Q: If 0 < a <1, then lim(a)* = x00

A:

Q: If lim f(x) = 7 and lim g(x) = -2, find the following. x→ 5 X→5

A: Since, we have been given limx→5f(x)=7 and limx→5g(x)=-2(a)…

Q: If 4x s g(x) < 2x- 2x2 + 4 for all x, evaluate lim g(x).

A:

Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: Find lim f (x) where 3 -{ * if a+3 if a = 3 f (1r) =

A:

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

A:

Q: is lim (x – 1) csc TX x→1 :Select one 1 .b - T.C 1 - .d

A:

Q: Define what it means to say that lim g(x) = k.                                              X-&gt;0

A: Given limit expression is limx→∞gx=k.

Q: Find lim [x csc(x)] as x approaches zero.

A:

Q: Evaluate each limit. (4х + 10 lim xS2 2х - 2

A: limx→24x+102x-2

Q: If 4x s g(x) s 2x* - 2x2 + 4 for all x, evaluate lim g(x). x-1

A: Given  4X &lt; g(x) &lt; 2x⁴-2x²+4 Now the lowe limit of the function should be equal to 4X because…

Q: evaluate lim f(x)- I-5

A: Given: The graph is as follows

Q: Find Lim x→ o" ( x-0

A:

Q: Find the one-sided limit

A: We need to find right hand limit, limx→0+6-1x3

Q: if 4x1

A: Given problem:-

Q: Use the graph to compute the quantities asked for. ... -3 -2 A. lim Ax) = %3D B. lim (x) = %3D

A:

Q: 1. For each statement, determine if it is True or False and explain why. x²-4 x-2 =x+2 b. lim *-* =…

A:

Q: If 2x < g(x) < x – x² + 2 for all x, evaluate lim g(x).

A: To evaluate: The limit limx→1gx. Given: The function is 2x≤gx≤x4-x2+2 for all x. Concept used:…

Q: Evaluate lim (1+x)/x x→0

A: Please see the answer in step 2

Q: Find the value of lim f(x), if x→7+ S8x + 2 x 7 f(æ) = 45 9. O 16 O 87 O 57

A:

Q: Divide numerator and denominator by the highest power of x in the denominator to find the limit |…

A:

Q: Evaluate lim x-i x - 1 1 using the appropriate change of variable.

A:

Q: for each positive number X Evaluate lim |

A: To evaluate the below limit for all the positive values of x. limn→∞1xn−x−n

Q: If 4x ≤ g(x) ≤ 2x4 − 2x2 + 4 for all x, evaluate lim x→1 g(x).

A: Now,

Q: x+4 Evaluate the following Imit: lim-* х-4 A) 1 B) Indefinite C) 0 D 2

A: We have to find the limit of the functions.

Q: If f(x) = 22 +1, then find lim f(x)-f(0)

A: Given, f(x)=2x2+1 ∴ f(0) = 0+1 = 1

Q: For any function f(x), If lim |f(x)| = , then lim f(x)=n %3D

A: Limit problem

Q: Evaluate lim(1+ tan x)r

A:

Q: If 6x ≤ g(x) ≤ 3x4 − 3x2 + 6 for all x, evaluate  lim x→1 g(x).

A:

Q: Evaluate lim I X - T

A:

Q: а) The function f is defined by 2, if x2 i) Find lim f(x). Give your reason.

A:

Q: Evaluate lim (e – 2x) -

A:

Q: Evaluate lim, o[cos()].

A:

Q: Find lim Vx-1 メー メーラ →o

A:

Q: Evaluate lim where k>0 X-k

A:

Q: Find the value of lim f(x), if 7x +2 x 5 f(x) = O 20 O 35 O 13 O 8 O 40

A: Solution:Givenf(x)=7x+2x≤53x+5x&gt;5To find:limx→5+f(x)

Q: lim 2 +and 2.

A: Explanation of the answer is as follows

Q: If f(x) = , find lim f(x).

A: Consider the given function, fx=e4x-19x apply limit, limx→∞fx=limx→∞e4x-19x=e4∞-19∞=1-10=00

Q: Evaluate lim x tan

A: Solving the problem by finding the limit of the expression.

Q: If 8x s g(x) < 4x4 - 4x2 + 8 for all x, evaluate lim g(x). X→1 1 Enhan

A:

Q: Evaluate lim x Inx². x→0+

A: We have to find the limit.                                   limx→0+xlnx2

Q: If lim x) - 2 x-1 x - 1 DNE lim f(x). = 7, evaluate

A:

Q: Evaluate I (n +) lim as n → ∞ VnT (n + 1)

A: Given: limn→∞Γn+32nΓn+1

Q: Evaluate lim is O -1/2 O 1

A: Given limx→2x2-4x2+4

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.