#### Differential Calculus Book Back Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If f(x) = x2 - x + 1, then f (x + 1) is

(a)

x2

(b)

x

(c)

1

(d)

x2 + x + 1

2. The graph of the line y = 3 is

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

3. Which one of the following functions has the property f (x) = $f\left( \frac { 1 }{ x } \right)$

(a)

$f\left( x \right) =\frac { { x }^{ 2 }-1 }{ x }$

(b)

$f\left( x \right) =\frac { 1-{ x }^{ 2 } }{ x }$

(c)

f(x) = x

(d)

$f\left( x \right) =\frac { { x }^{ 2 }+1 }{ x }$

4. The range of f(x) = |x|, for all $x\epsilon R$, is

(a)

(0, $\infty$)

(b)

(0, $\infty$)

(c)

(-$\infty$$\infty$)

(d)

(1, $\infty$)

5. A function f(x) is continuous at x = a if $\lim _{ x\rightarrow a }{ f\left( x \right) }$ is equal to

(a)

f(-a)

(b)

f$(\frac{1}{a})$

(c)

2f(a)

(d)

f(a)

6. 3 x 2 = 6
7. Determine whether the following functions are odd or even?
f(x) = x2-|x|

8. If f(x) = 2x, show that f(x) . f(y) = f(x + y)

9. Evaluate: $\underset { x\rightarrow a }{ lim } \frac { { x }^{ \frac { 3 }{ 5 } }-{ a }^{ \frac { 3 }{ 5 } } }{ { x }^{ \frac { 1 }{ 5 } }-{ a }^{ \frac { 1 }{ 5 } } }$

10. 3 x 3 = 9
11. Differentiate sin2 x with respect to x2.

12. If $\lim _{ x\leftarrow 2 }{ \frac { { x }^{ n }-2^{ n } }{ x-2 } =448 }$ ,then find the least positive integer n

13. Draw the graph y = 9 - x2

14. 2 x 5 = 10
15. Draw the graph of the following function $f(x)=\frac { |x| }{ x }$

16. Darw the graph of f(x) = logax; x > 0, a > 0 and $a\ne 1$.