Evaluate limits by substitution or by factorising

Question 1

Find lim(x→1) (x² − 1)/(x² + 5x − 6). Give a fraction if needed.

Answer (as a fraction)

Question 2

Find lim(x→4) (2x² − 3x − 6).

Answer 

Question 3

Find lim(x→−6) (x² + 5x − 6)/(x + 6).

Answer 

Question 4

Find lim(x→4) (x² − 16)/(x² + 2x − 24). Give a fraction if needed.

Answer (as a fraction)

Question 5

Find lim(x→0) (2x² + x + 7).

Answer 

Question 6

Find lim(x→6) (x² − 7x + 6)/(x − 6).

Answer 

Question 7

Find lim(x→2) (x² − 4)/(x² − 8x + 12). Give a fraction if needed.

Answer (as a fraction)

Question 8

Find lim(x→−1) (x² + 3x − 3).

Answer 

Question 9

Find lim(x→−4) (x² + 10x + 24)/(x + 4).

Answer 

Question 10

Find lim(x→−4) (x² − 16)/(x² + 7x + 12). Give a fraction if needed.

Answer (as a fraction)

Question 11

Find lim(x→1) (2x² − 6x + 8).

Answer 

Question 12

Find lim(x→2) (x² − 7x + 10)/(x − 2).

Answer 

Question 13

Find lim(x→−4) (x² − 16)/(x² + 6x + 8). Give a fraction if needed.

Answer (as a fraction)

Question 14

Find lim(x→0) (x² + 5x − 2).

Answer 

Question 15

Find lim(x→4) (x² − 10x + 24)/(x − 4).

Answer 

Question 16

Find lim(x→−3) (x² − 9)/(x² + 7x + 12). Give a fraction if needed.

Answer (as a fraction)