Let `f(x) = (x-a) cos (1/(x-a))` for `x ne a ` and let f(a) = 0.
Show that f is not derivable at `a` .

Let f(x) = (x - a) cos (1/(x-a)) for x ne a and le f (a) = 0. Show that f is continuous at x = a but not derivable thereat.

Let f(x) = (x+|x|)/x for x ne 0 and let f (0) = 0, Is f continuous at 0?

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

Let f(x) = |x| cos (1/x) for x ne 0 . Write the down the value of (f) (0) if f is continuous at x = 0

Let f(x) = (log(1+x))/(sinx) for x ne 0 . Find f(0) if f is continuous at x = 0

Let f= R rarr R be defined by f(x)=3x-7. Show that f is invertible.

If f(x) = (|x-4|)/(4-x), x ne 4, f(4) = 0 , show that f is continuous every where except at x = 4.

Let f(x) = (2^(1/x))/(1+2^(1/x)) for x ne 0 . Find f(0) if f is right continuous at x = 0

Let f : R rarr R be defined by f(X) = 10 x + 7. Show that f is invertible. Find f^-1

Let f(x) = {:{((sinx)/x + cosx, when x ne 0),(2, when x = 0):} show that f (x) is continouous at x = 0.