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Answers
Limits and Derivatives
Exercise 13.1P.301
Q.1: Evaluate the Given limit: limx→3x+3
Ans : limx→3x+3=3+3=6
Q.2: Evaluate the Given limit: limx→π(x−
22
7
)
Ans : limx→π(x−
22
7
)=(π−
22
7
)
Q.3: Evaluate the Given limit: limr→1πr2
Ans : limr→1πr2=π(1)2=π
Q.4: Evaluate the Given limit: limx→4
4x+3
x−2
Ans : limx→4
4x+3
x−2
=
4(4)+3
4−2
=
16+3
2
=
19
2
Q.5: Evaluate the Given limit: limx→−1
x10+x5+1
x−1
Ans : limx→−1
x10+x5+1
x−1
=
(−1)10+(−1)5+1
−1−1
=
1−1+1
−2
=−
1
2
Q.6: Evaluate the Given limit: limx→0
(x+1)5−1
x
Ans : limx→0
(x+1)5−1
x
Put x + 1 = y so that y → 1 as x → 0.
Accordingly, lim
(x+1)5−1
x
= limy→1
y5−1
y−1
= limy→1
y5−15
y−1
=5.15−1[limx→a
xn−an
x−a
=nan−1]
=5
∴limx→0
(x+5)5−1
x
=5
Q.7: Evaluate the Given limit: limx→2
3x2−x−10
x2−4
Ans : At x = 2, the value of the given rational function takes the form
0
0
∴ limx→2
3x2−x−10
x2−4
= limx→2
(x−2)(3x+5)
(x−2)(x+2)
= limx→2
3x+5
x+2
=
3(2)+5
2+2
=
11
4