show that If an > 0, n = 1, 2,. .... In+1 In+1 lim inf 14x

Q: L3x* -3x +b for all X, If bx < alx) evaluate lim 96x)

A: Concept:

Q: Inx L'hopital rule does not apply to lim x--o x False O True

A:

Q: (c) lim √n! = ∞. n→∞0

A: To show that limn→∞ n!n=∞

Q: 6. Evaluate lim r/(1-z) 2+1+

A:

Q: The real roots of 25x + bx² - c = 0 if b = 6 and c = 7 can be determined using Fixed Point Iteration…

A:

Q: 3. a) Find the following limits. (Don't use L'hôpital Rule.) |x+3| x+3 |x+3|| lim x-3x+3 =? x-1 x-1…

A:

Q: Show that |x2-4|&lt;e ,  when 0&lt;|x-2|&lt;e(5+e)-1 and prove limx-&gt;2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

Q: Prove that lim 1 H 101H 818

A: We have to prove that  limx→0- 1x → -∞.

Q: Use numerical evidence to evaluate lim (5. (5. √x + 4) x18 f(x) X 1 100 10000 1000000 Type in oo for…

A: By using numerical evidence to evaluate the following limit. limx→∞5·x+4

Q: (1+x)* - b. Evaluate lim

A:

Q: e following is the definition for limx->a f(x) = L: For every real number ε > 0, there exists a real…

A: we know that Negation of statement A⇒B is  ~(A⇒B)↔~(~A∨B)↔~~A∧~B↔A∧~B so, Now we will find the…

Q: What is wrong with the following x³ + x lim x1 x²-3x+2 proof"? Give the correct version. 2 3x² +1…

A:

Q: 32. Evaluate: lim X18 10 (x + 1)¹⁰ + (x + 2)¹0 + 10 X + (x + 2012) ¹0 ... + 2012¹0

A:

Q: Prove lim x³ = X→3 27 using the 8, & definition of limits.

A:

Q: Prove that lim n = p.

A:

Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: Prove that lim sin( nx) + n dx= In 2 . (n+) Explain your answer carefully

A:

Q: 1 Assume that lim xn +oo. Prove that lim n-00 n +o0. n-00 k=1

A: Given limn→∞xn=+∞

Q: Late 73. Use Definition 6 to prove that lim —— 0.

A:

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax