State whether the following statements are true or false. Give reasons for your answers.
(i)
(ii) A real-valued function of three variables which is continuous everywhere is differentiable.
(iii) The function is locally invertible at any
(iv)
is integrable.
(v) The function (.0,0)
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Find the following limits:
(i)
(ii)
Find the third Taylor polynomial of the function
Find the values of a and b, if
Identify the level curves of the following functions:
(i)
(ii)
(iii) x-y
(iv) y/x
)1,4 be three points in . R3
Find |2 b − a + 3c l.
be a continuously differentiable function of x and y, whose partial derivatives are also continuously differentiable. Show that
Let the function f be defined by
Show that f has directional derivatives in all directions at.(0,0)