Urgent Help Needed.

Hi, I need urgent help with multiple questions, mostly deaing with limits and other small easier problems.
I really have no idea how to solve limits at this point but will have to learn the hard way.

solve by substitution:

lim (2x^2-4x+7,x,5)

Please show me how to solve it. The answer is 37 I think but I don't know how to solve it without using my TI-89

Find lim (x^2+x-6)/(x-2),x,2] <- if it exists

Find Lim [(X+3)/(X-3),x,3]

Thanks :)

To solve thissolve by

To solve this

solve by substitution:

lim (2x^2-4x+7,x,5)

Please show me how to solve it. The answer is 37

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Just put the value of x as 5 in the above expression

 

( 2 * 5^2 -5*4 +7)

( 2*25 -20+7)

( 50-20+7)

= 37

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Find lim (x^2+x-6)/(x-2),x,2] <- if it exists

Find Lim [(X+3)/(X-3),x,3]

 

To solve the above two questions just use L hospital rule and take derivative on both numberator and denimominator

then put value of x as required

lets take first part

Find lim (x^2+x-6)/(x-2),x,2]

Taking derivative on both numerator and den

2x+1/1

 

Putting x = 2

2*2+1 = 5 Answer

Now just do the third part

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