MTH101 Midterm Unsolved Paper 4

MTH101 - Calculus And Analytical Geometry

Q1. If f is a twice differentiable function at a stationary point (1 marks)

0x and

f

x

then f has

relative …………. At 0x

Minima Maxima

Q2. If f is a twice differentiable function at a stationary point (1 marks)

0x and

f

x

then f has

relative …………. At 0x

Minima Maxima

Q3. A line (1 marks)

y

y

is called a ………………. for the graph f if

lim

lim

x x

f x · y · or · f x · y

Vertical asymptotes Horizontal asymptotes

Q4. If (1 marks)

f x x x then f x

x +

x +

x x

x x

Q5. (sec (1 marks)

d x dx

sec tan x x

sec tan x x

sec t co x co x

Q9. If (1 marks)

y f g h x

u g h x

v h x

then dy dx =

dy du dv du dv dx

dy du dv du dv dx

dv du dy du dv dx

Q10. d (1 marks)

f g x dx

f g x f x

f g x g x

f g x g x

f g x g x

Q11. Please choose one Chain rule is a rule for differentiating ___________ of functions. Product (1 marks)

Sum Difference Composition

Q12. Please choose one 1x and (1 marks)

f x f x whenever x x

correct?

1. f is an increasing function.
2. f is a decreasing function.
3. f is a constant function.

Q13. Please choose one 1x and (1 marks)

f x f x whenever x x

correct?

1. f is an increasing function.
2. f is a decreasing function.
3. f is a constant function.

Q14. If (1 marks)

f x on an open interval (a,b) then which of the following statement is correct?

1. f is concave up on (a, b).
2. f is concave down on (a, b)
3. f is linear on (a, b).

Q15. [ln ] (1 marks)

d · If x · then · x

dx

1. x

x

ln x

Q16. x (1 marks)

d · If b · then · b · dx

x

xb

1. ln b

ln

xb

b

Q17. [ln2 ] (1 marks)

d · If · x · then · x · dx · x