limit of  x² + 6x- 7 as x

shaaaaane.shane

shaaaaane.shane

Answered question

2022-04-18

limit of  x² + 6x- 7 as x approaches – 2 

Answer & Explanation

Gulsade Cakmak

Gulsade Cakmak

Beginner2022-06-06Added 1 answers

 limx-2x2+6x-7 = (-2)2 +6*(-2) -7 = 4-12-7=-15

Substitute x with (-2)

Note: In polynomial functions, if the x-value (here, -2) does not make the expression undefined, limit of that expression is calculated by substituting the variable (x=-2) with given value.

For polynomial functions:

limxaf(x) = f(a)   if and only if f(a) undefined 

nick1337

nick1337

Expert2022-07-01Added 777 answers

limx-2x2+6x-7

Split the limit using the Sum of Limits Rule on the limit as xx approaches -2.

limx-2x2+limx-26x-limx-27

Move the exponent 2 from x2 outside the limit using the Limits Power Rule.

(limx-2x)2+limx-26x-limx-27

Move the term 6 outside of the limit because it is constant with respect to x.

(limx-2x)2+6limx-2x-limx-27

Evaluate the limit of 7 which is constant as xx approaches -2.

(limx-2x)2+6limx-2x-17

Evaluate the limits by plugging in -2 for all occurrences of x.

Evaluate the limit of xx by plugging in -2 for x.

(-2)2+6limx-2x-17

Evaluate the limit of x by plugging in -2 for x.

(-2)2+6-2-17

Simplify the answer.

Simplify each term.

4-12-7

Subtract 12 from 4.

-8-7

Subtract 7 from -8.

15

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