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Question

Q1. If f(x) = 4x² - 24, then find

(a) 20 (b) 22 (c) 23 (d) 24

Q2. Find

log x - log 5/ x - 5

=

log

x/ 5

/x - 5

=

log(1 +

x/ 5

- 1)/ x - 5

log(1 +

x - 5/5

) /(

x - 5/ 5

) . 5

=

1 /5

Q3. Find
(a) 1/e (b) 1 (c) e (d)2

Q4.
(a) 6 (b) 7 (c) 8 (d) 9

Q5. Evaluate

9x cosx - 4sinx /5x + 3tanx

Solution.
=

(

9x cosx - 4sinx /x

) / (

5x + 3tanx /x

)

=

9cosx -

4sinx /x

/5 +

3tanx /x

=

9 - 4/5 + 3

=

5/8

Q6. Evaluate

4x + lxl/ 9x - 7lxl

(a) 1 (b) 1/2 (c) 5/2 (d) limit does't exist

Solution.
LHL =

4x - x/ 9x + 7x

=

3x/ 16x

=

3/ 16

RHL =

4x + x/ 9x - 7x

=

5x/ 2x

=

5/ 2

LHL ≠ RHL

Q7. Evaluate

1 /x²

(1 + 2 + 3 + --------+ x) .

Solution.
=

1 /x²

∑ x =

x(x + 1) /2x²

=

x + 1 /2x

(

x /2x

+

1 /2x

) =

1/2

+

1 /2x

=

1/2

Q8.

4^x - 2^x /x

Solution.

4^x - 2^x /x

= 2^x

2^x - 1 /x

= 2⁰ . log_e2 = log_e2

Q9.

1³ + 2³ + 3³ + --------- + n³ /n⁴

=

Q10.

e^x - e^-x /x

=

Solution.

e^x - e^-x /x

=

e^x -

1 /e^x

/x

= 2 (

e^2x - 1 /2x

) (

1 /e^x

)

= 2