Limits Practice Problems With Key

Limits Problems and solutions Level -1
Choose the Correct Answer :
1)
Lt
x→3
{2x² –3x –5}=
4
3
–4
–3
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Lt
x→3
{2x² –3x –5}= 2(3)² –3(3) –5
=18 –9 –5=4
2)
Lt
x→3
x²+2x–5
2x²–5x+1
5/2
2/5
7/5
4/5
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Lt
x→3
x²+2x–5
2x²–5x+1
=
(3)²+2(3) –5
2(3)² –5(3)+1
=10/4=5/2
3)
Lt
x→1
x²–3x+2
x²–4x+3
3/4
4/3
2/3
1/2
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Lt
x→1
x²–3x+2
x²–4x+3
(0/0)=
Lt
x→1
2x–3
2x–4
{∵ differentiate in numerator and denominator}
= (–1)/ (–2)=1/2
4)
Lt
x→2
7x²–11x–6
3x²–x–10
7/2
17/11
7/36
–7/3
Click here to check answer
Lt
x→2
7x²–11x–6
3x²–x–10
(0/0)=
Lt
x→2
14x–11
6x–1
{∵ differentiate in numerator and denominator}
= [14(2)–11]/[6(2)–1]=17/11
5)
Lt
x→–1
x+1
√x²+3 –2
=
2
3
–2
–3
Click here to check answer
Lt
x→–1
x+1
√x²+3 –2

=
Lt
x→–1
1
2x/(2√x²+3)
 =–2

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