x²-9 lim is equal to: х->3 х-3 а) 2 b) 3 с) 6

Q: 1. If f(r) = , do the following: %3D iii) What is lim

A: Given Function, f(x)=1x

Q: Evaluate using the Squeeze Theorem

A: To Evaluate: limx→0xsin1x2 Concept: Squeeze Theorem:limx→afx≤limx→agx≤limx→ahxand if…

Q: sin 7x lim x→0 sin 3x

A: The given limit is limx→0sin7xsin3x

Q: evaluate using Theorem 2 as necessary.

A:

Q: 3. Evaluate lim, tan (2 x) if it exists. Provide evidence to back up your answer.

A:

Q: Given that    lim x→4 (4x − 13) = 3,    illustrate Definition 2 by finding values of delta that…

A:

Q: What is lim m→0 sin(m) m ?

A:

Q: Prove the lim(Sn) = -∞ case.

A: We use the notation uN =inf{ sn :n>N},              vN =sup{ sN : n>N }, u = lim uN = lim inf…

Q: Prove that lim 1 1 by definition.

A: To prove- limn→∞1-1n=1 Here , Let y=1/n We will construct a table for the values of n and y.

Q: +2 dt 8. lim 7x

A:

Q: Prove that lim, = 1, (x > 0).

A:

Q: lim x* cos 1 = 0 .5

A: Show that , limx→0x4cos1x5=0

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

A:

Q: Prove that lim, Vn = 1.

A:

Q: sec x lim sec(3x)

A:

Q: What is lim In x? x→2

A:

Q: Use the results of Section 2.2 to evaluate lim (5x – 3 0.2545454545 x-3 11 symbolic formatting help

A: To evaluate the given limit.

Q: Show that the following: If r > 1, then lim Vr – 1 = 0.

A:

Q: rasb then prove Lim Ja 9. that

A: If  0<a<b  then prove that limn→∞an+bnn=b

Q: Find the limit or enter DNE if the limit does not ex lim エー10 VI-9-7 エ-58

A:

Q: Assume lim,→a f (x) = L. If f(x) > k, prove that L > k. Prove by con- tradiction by assuming L < k…

A:

Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Evaluate: lim, (cos z). Show your solution. O -1

A: Limit of a function f(x) at point x = a exists only when Left hand Limit(LHL) = Right hand limit…

Q: Evaluate the limit: lim 10x2 cos(4x) 10

A:

Q: find the limit or explain why it does not exist

A: To find the limit.

Q: Find the limits in Exercise

A: Given,          limx→-1416x13x+162

Q: 4. Use the e, 8 definition to show that lim,- (4x + 5) = 9.

A:

Q: Use a table of values (on your calculator) to estimate the value of the limit to at least 2 decimal…

A: Given, limx→1x2+4x-5x-1 Using table of values,  we have to estimate the value of the limit at least…

Q: 5. Find the following limits. (a) lim,0 EE. 22-iz-1-i (b) limz→1+i z2–22+2 °

A: Apply the limits.

Q: Find the limits in Exercise

A: Given, limx→-12x3-5x2+3x+5 function is continous so find limit of function at x=-1…

Q: Let a and b be positive real numbers. Evaluate lim (ax – Vax – bx) in terms of a and b.

A: To evaluate limx→∞ax-a2x2-bx where a and b are positive real number

Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: Exercise 6. Find the limits. lim n sin dx.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: evaluate using the Squeeze Theorem.

A: We know that sin is always  between -1 to 1 Multiply all sides by (x-1) and then take limit x-&gt;…

Q: If(z)- 니 < e. By definition Show that: lim, »1+i = - а. b. 4 lim = 2i. %3D 2- 1-i z2

A:

Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: Find the limit. lim sin P-(8, 0, -8) TT 1, OOO

A: To find the limit:                          limP→8,0,-8ey2sin-1-zx

Q: Let m and n be two positive integers greater than 1. ecos (α"). am m then the value of (1) is n If…

A:

Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: Using the squeeze theorem, find the value of lim,0 x² sin=) O 1 O -1 O does not exist

A:

Q: Solve the following limits. (a) lim r In x (b) lim 2+ sec (3x) (c) lim 7/6 tan (3I) –1

A:

Q: (1 cosrjir lim,o = ?

A:

Q: Exercise 6. Find the limits. sin (=)dr lim lim 1+r2n xp- lim n Jo (1+ =)"dz. dr.

A: A function is said to be bounded if it's upper bound and lower bound exist. We will use Lebesgue…

Q: 2) G VALUATE THE UMIT, IF IT EXISTS. Lim X-3 x2-X-12 uT x²+ 3x 2)

A: Given:         limx→-3x2+3xx2-x-12   Factoring                   =limx→-3xx+3x-4x+3

Q: Evaluate the limit. ΣΗ. 2i + 1 lim i=1 =W

A:

Q: Prove that lim Vr = 2 using the e-d-definition. Hint: VI - 2 = x - 4 %3D VI+2°

A:

Q: lim 1-3 (r-3) tan(9-x²) sin²(2x - 6)

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: O Evaluate the lim x sin (-), (Use Squeeze Theorem) 1-0

A: Given : The limit is limx→0 x sin 1x .

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.