
Find the linit and prove it using the defination lim 3 x² + 5 at tat
3. (10 marks) Find the limit and prove it using the definition. 3x2 + 5 lim x=0x2 + x + 1
3) Find the limit and prove it using definition lim 4x² + 13 x 70 x² + xt I
3. (10 marks) Find the limit and prove it using the definition. 4x2 + 13 lim x+ x2 + x + 1 4. (10 marks) Find the limit and prove it using the definition. 4x3 + 13 lim *40x2 + x + 1
3. (10 marks) Find the limit and prove it using the definition. 4x2 + 13 lim x2 + x +1 X-700
f(x)-3 If lim – - = 2, find lim f(x). X-5 X-3 X- 5 lim f(x) = X-5 (Type an integer or a simplified fraction.)
Prove that lim ((2x+3)/(x^2 +5))=1/2 as x approaches 2.
Given that lim f(x) = 3, lim g(x) = 0, and lim h(x) = 5, find the limits that exist. Enter DNE if the limit doesn't exist help (limits) (a) lim f(x) + h(x)] = 8 (b) lim{f(x)} = 9 (c) lim yh(x) = 5^(1/3) help (limits) !!! help (limits) help (limits) In help (limits) help (limits) f(3) (2) (9) lim !!! help (limits) 3-a g(x) 2f(x) !! help (limits) h(x) - f(x)
3 Use the 2-3 definition of lim f(x)=1 to prove that lim x+8 = 14.
4. (10 marks) Find the limit and prove it using the definition. 4x3 + 13 lim x70x2 + x +1
3) Complete the following to prove lim (4x – 3)= 5 using the epsilon-delta definition of a limit. x2 Part 1: Analysis (i.e. "guess” a 8) For every we need to if then (Complete these steps as you want in order to find delta.) This suggests that we should choose Part 2: Proof: (show that this choice of satisfies the definition of a limit). Given choose If then Thus, if , then Therefore, by Q.E.D.