Find the length of the curve y = In 
from x = 1 to x = 2
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The cost of fuel is running an engine is proportional to the square of the speed in km/h and is ` Rs 48 per hour when the speed is 16 km/h. Other costs amount to ` Rs300 per hour. Find the most economical speed.
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she begins by running at a constant speed till she reaches a hilly portion 2 km from her home. Here her speed slows down while she runs up the hill, which is a 1-km run. Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance from her home. Also find the range of this function.
Find the maxima and minima, if any, for the function f given by
f (x) = x4 - 14x2 + 24x + 6.
Also find the values of the function at those points.
Differentiate cos-1 (2x 2 -1) with respect to sin-1 squr(1 - x 2 ).
- hich of the following statements are true or false? Give reasons for your answers.
- The greatest integer function is continuous on R .
- The domain of the function f , given by
iii) The function f , defined by f (x) = x 3 - 6x 2 + 16x - 15, is increasing in R .
iv) Rolle’s theorem is applicable for the function f , defined by
f (x) = 1 + x 2 /3 in the interval [-1,1].v)
Give an example of a function which is one to one but not onto, with reason.
Find the length of the curve y = In from x = 1 to x = 2