If f(x) = Sin(x)Cos(x) is continuous and differentiable in interval (0, x) then

1< ( frac{Cos(x)Sin(x)}{x} ) <xCos(2x)

1< ( frac{Cos(x)Sin(x)}{x} ) <Sin(2x)

1< ( frac{Cos(x)Sin(x)}{x} ) <Cos(2x)

1< ( frac{Cos(x)Sin(x)}{x} ) <xCos(2x)

1< ( frac{Cos(x)Sin(x)}{x} ) <1+Cos(2x)

Mean Value Theorem tells about the

Existence of point c in a curve where slope of a tangent to curve is equal to zero

Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable

Existence of point c in a curve where slope of a tangent to curve is equal to zero

Existence of point c in a curve where curve meets y axis

Existence of point c in a curve where curve meets x axis

Explore topic-wise MCQs in Engineering Mathematics.

This section includes 6 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.	If f(x) = Sin(x)Cos(x) is continuous and differentiable in interval (0, x) then
A.	1< ( frac{Cos(x)Sin(x)}{x} ) <Sin(2x)
B.	1< ( frac{Cos(x)Sin(x)}{x} ) <Cos(2x)
C.	1< ( frac{Cos(x)Sin(x)}{x} ) <xCos(2x)
D.	1< ( frac{Cos(x)Sin(x)}{x} ) <1+Cos(2x)
Answer» C. 1< ( frac{Cos(x)Sin(x)}{x} ) <xCos(2x)

Discussion

2.	Find point c between [-1,6] where, the slope of tangent to the function f(x) = x²+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)). (Providing given function is continuous and differentiable in given interval).
A.	2.5
B.	0.5
C.	-0.5
D.	-2.5
Answer» B. 0.5

Discussion

3.	Find point c between [2,9] where, the slope of tangent to the function f(x)=1+ ( sqrt[3]{x-1} ) at point c is equals to the slope of a line joining point (2,f(2)) and (9,f(9)). (Providing given function is continuous and differentiable in given interval).
A.	-2.54
B.	4.56
C.	4.0
D.	4.9
Answer» C. 4.0

Discussion

4.	Can Mean Value Theorem be applied in the curve f(x)= ( begin{cases}3sin(x)&0<x< pi/4 sin(x)-cos(x)& pi/4<x< pi/2 end{cases} )
A.	True
B.	False
Answer» C.

Discussion

5.	Find the equation of curve whose roots gives the point which lies in the curve f(x) = xSin(x) in the interval [0, ₂] where slope of a tangent to a curve is equals to the slope of a line joining (0, ₂)
A.	c = -Sec(c) Tan(c)
B.	c = -Sec(c) Tan(c)
C.	c = Sec(c) +Tan(c)
D.	c = Sec(c) Tan(c)
Answer» E.

Discussion

6.	Mean Value Theorem tells about the
A.	Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable
B.	Existence of point c in a curve where slope of a tangent to curve is equal to zero
C.	Existence of point c in a curve where curve meets y axis
D.	Existence of point c in a curve where curve meets x axis
Answer» B. Existence of point c in a curve where slope of a tangent to curve is equal to zero

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

If f(x) = Sin(x)Cos(x) is continuous and differentiable in interval (0, x) then

Find point c between [-1,6] where, the slope of tangent to the function f(x) = x2+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)).(Providing given function is continuous and differentiable in given interval).

Find point c between [2,9] where, the slope of tangent to the function f(x)=1+ ( sqrt[3]{x-1} ) at point c is equals to the slope of a line joining point (2,f(2)) and (9,f(9)).(Providing given function is continuous and differentiable in given interval).

Can Mean Value Theorem be applied in the curvef(x)= ( begin{cases}3sin(x)&0<x< pi/4 sin(x)-cos(x)& pi/4<x< pi/2 end{cases} )

Find the equation of curve whose roots gives the point which lies in the curve f(x) = xSin(x) in the interval [0, 2] where slope of a tangent to a curve is equals to the slope of a line joining (0, 2)

Mean Value Theorem tells about the

Find point c between [-1,6] where, the slope of tangent to the function f(x) = x²+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)).
(Providing given function is continuous and differentiable in given interval).

Find point c between [2,9] where, the slope of tangent to the function f(x)=1+ ( sqrt[3]{x-1} ) at point c is equals to the slope of a line joining point (2,f(2)) and (9,f(9)).
(Providing given function is continuous and differentiable in given interval).

Can Mean Value Theorem be applied in the curve
f(x)= ( begin{cases}3sin(x)&0<x< pi/4 sin(x)-cos(x)& pi/4<x< pi/2 end{cases} )

Find the equation of curve whose roots gives the point which lies in the curve f(x) = xSin(x) in the interval [0, ₂] where slope of a tangent to a curve is equals to the slope of a line joining (0, ₂)