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solve this question of limits and derivative​

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Answered by suraj6515
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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

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