If y = emtan -1 x , show that (1 + x2 ) y n+1 (2nx - m) yn n(n -1)y n -1 = 0.
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For which value(s) of k, is the function f, defined as below, continuous at x = 2?
Further, at which other points in [1, ∞ [ is f continuous, and why?
Differentiate tan -1 [sin x - cos x /sin x + cos x]
with respect to 1/2 x.
- 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)
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.
If y = emtan -1 x , show that (1 + x2 ) y n+1 (2nx - m) yn n(n -1)y n -1 = 0.
Find the volume of the solid obtained by revolving the curve
X = a cos3 θ , y = a sin 3 θ about the y-axis.
Prove that 