applied functional analysis

Various forms of complex numbers Mathematical induction Roots and poles of rational functions Graphing rational functions - asymptotes Limits of sequence/function..

If a quantity is dependent on trigonometric or exponential functions, this method cannot be use..

Dimensional analysis has no information on dimensionless constants. If a quantity is dependent on trigonometric or exponential functions, this method cannot be used. In some cases, it is difficult to guess the factors while deriving the relation connecting two or more ph..

Select the statement that explains why the mean value theorem does not apply to the function f ( x ) = tan x in the interval [0, π ]. => tan x is continuous in [0, π ]. or tan x is not continuous in [0, π ]. or tan x is not differentiable in (0, π ). or both B & C..

Which statement explains why the mean value theorem does not apply to the function f ( x ) = | x | x in the interval [-2, 2]? => there exists c ∈ [-2, 2] such that f ′ ( c ) = 0 or f ( x ) is differentiable in [-2, 2] or f ( x ) is not continu..

Which of the following transformations has to be applied to the graph of the function f ( x ) = 3 x to get the graph of g ( x ) = 3 2 x ? => Horizontal shrinking by a factor of 2 or Vertically stretching by a factor of 9 or Shifting 9 units vertically up or Horizontal stretching..

Which of the following transformation has to be applied to the graph of the function f ( x ) = ln x to get the graph of g ( x ) = 32 ln x ? => Vertical shrink, by a factor of 32 or Vertical stretch, by a factor of 1 32 or Vertical stretch, by a factor of 32 or Horizontal stretch..

Which of the following transformations has to be applied to the graph of the function h ( x ) = 9 x to get the graph of g ( x ) = 9 - x ? => Vertical shrinking by a factor of 1 or Reflecting the graph of h ( x ) = 9 x across y - axis or Reflecting the gr..

Which of the following transformations have to be applied to the graph of reciprocal function f ( x ) = 1 x to get the graph of g ( x ) = 5 x - 2 9 x - 6 ? => Translation to the right by 5 unit and then translation vertically up by 6 units. or Translation to the right by 6 unit ..

Which of the following transformations have to be applied to the graph of reciprocal function f ( x ) = 1 x to obtain the graph of g ( x ) = 8 8 - 9 x x - 1 0 ? => Translation to the right by 10 units followed by a reflection about y -axis. or Translation to the right 10 units, ..