Question

Evaluate the following :

$space space space space space space space limit as straight x rightwards arrow of left parenthesis 3 minus straight x squared right parenthesis$

Solution

$space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 1 of left parenthesis 3 minus straight x squared right parenthesis space equals limit as straight x rightwards arrow 1 of 3 minus limit as straight x rightwards arrow 1 of straight x squared equals 3 minus left parenthesis 1 right parenthesis squared equals 3 minus 1 equals 2$

Question

Wired Faculty App

Evaluate the following :

$WiredFaculty$

Solution

$space space space space space space space space space space space space space space space limit as straight x rightwards arrow 4 of left square bracket straight x left parenthesis straight x plus 1 right parenthesis right square bracket space equals space open parentheses limit as straight x rightwards arrow 4 of space straight x close parentheses. open parentheses limit as straight x rightwards arrow 4 of left parenthesis straight x plus 1 right parenthesis close parentheses equals 4 open parentheses limit as straight x rightwards arrow 4 of straight x plus limit as straight x rightwards arrow 4 of 1 close parentheses equals 4 left parenthesis 4 plus 1 right parenthesis equals 4 left parenthesis 5 right parenthesis equals 20$

Question

Wired Faculty App

Evaluate the following :

$WiredFaculty$

Solution

$space space space space space limit as space space straight x rightwards arrow negative 1 of left parenthesis 1 plus straight x plus straight x squared plus...... space plus space straight x squared right parenthesis space equals stack lim space space left parenthesis 1 right parenthesis with straight x rightwards arrow negative 1 below plus limit as straight x rightwards arrow negative 1 of left parenthesis straight x right parenthesis space plus space limit as straight x rightwards arrow negative 1 of straight x squared plus space...... plus space limit as straight x rightwards arrow negative 1 of straight x to the power of 12$
= 1 + (-1) + (-1)²+ .... + (-1)¹²= 1 + (-1) + 1 + ..... + 1 = 1

Question

Wired Faculty App

Evaluate $WiredFaculty$

Solution

$space space space space space space space space space space space space space space space space space space limit as straight x rightwards arrow 4 of fraction numerator 4 straight x plus 3 over denominator straight x minus 2 end fraction equals fraction numerator 4 left parenthesis 4 right parenthesis plus 3 over denominator 4 minus 2 end fraction equals fraction numerator 16 plus 3 over denominator 2 end fraction equals 19 over 2$

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Limits and Derivatives

Evaluate the following :

$space space space space space space space limit as straight x rightwards arrow of left parenthesis 3 minus straight x squared right parenthesis$

Evaluate the following :

$WiredFaculty$

Evaluate the following :

$WiredFaculty$

Evaluate $WiredFaculty$

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