Thursday

December 18, 2014

December 18, 2014

Posted by **Lexi** on Wednesday, May 16, 2012 at 12:41pm.

1. Find the limit by numerical evidence of limx -->4 x3+4x2-7x-5

2. Find the limit of limx-->-9 x2-81x+9.

3. Find the limit of each of the following:

a. limx-->0 x+4x-2x

b. limx-->0 x3+51 x2-17

c. limn-->infinity 1+1nn

d. limx-->0 sinxx

- Calculus -
**Steve**, Wednesday, May 16, 2012 at 3:43pm#1.

f(3.000000) = 37.000000

f(3.900000) = 87.859000

f(3.990000) = 94.271599

f(3.999000) = 94.927016

f(3.999900) = 94.992700

f(3.999990) = 94.999270

f(3.999999) = 94.999927

Looks like lim = 95, eh?

do #2 likewise

for lim sin(x)/x use L'Hopital's Rule

lim sinx/x = lim cosx/1 = 1

---------------------

lim [1 + (1/x)]^x ...... it is understood that x approaches infinity

= lim e^ln( [1 + (1/x)]^x )

= e^ ( lim ln( [1 + (1/x)]^x ))

= e^ ( lim x * ln[1 + (1/x)] )

= e^ ( lim ln[1 + (1/x)] / (1/x) ) .. the limit is now 0/0 ...

..... by L'Hopitals Rule

= e^ ( lim {1/[1 + 1/x] *(-1/x^2)} / {-1/x^2} )

= e^ lim 1/[1+1/x]

= e^1

= e.

**Answer this Question**

**Related Questions**

Calculus - 1. Does the limit limx-->0:6[[x]] exist? 2. Does the limit limx--&...

Math - Prove the theorem that if limx¡úd h(x)= P and limx¡úd k(x) = Q and h(x...

Calculus - Find the limit as x approaches infinity of (lnx)^(1/x). This unit is ...

Calculus - Evaluate the following limit: lim x->0 xcscx =limx->0 x/sinx ...

calculus - Find the following limit where f(x) = 4x2 − 3x. limit delta x...

math - How to solve for delta using trig functions? i.e. cosine sine tangent ...

Calculus - Consider the function f(x)=(4^x−1)/x. (a) Fill in the ...

Calculus - Consider the function f(x)=(4^x−1)/x. (a) Fill in the ...

Calculus - f(x) = {x^3 - 1, x> or equal to -1 {2x,x<-1 find limit x->-1...

calculus - What analytic method steps are required to find the limit of cos x-1/...