6.Find the limitlim_{x to infty} (e^{-2x} cos x)7.Find the limitlim_{x to (9pi/2)^+} e^{tan x}

Question

Drew Patel · Accepted Answer

6.       lim          x      →      ∞        (      e          −      2      x        cos  ⁡  x  )Using squeeze theorem  −  1  ≤  cos  ⁡  x  ≤  1  −      e          −      2      x        ≤      e          −      2      x        cos  ⁡  x  ≤      e          −      2      x            lim          x      →      ∞        (  −      e          −      2      x        )  =  −      e          −      2      ×      ∞        =  −      e          −      ∞        =  −      1          e              ∞              =  −      1          (      very very huge number      )            lim          x      →      ∞        (  −      e          −      2      x        )  =  0and       lim          x      →      ∞        (      e          −      2      x        )  =      e          −      2      ×      ∞        =      e          −      ∞        =      1          e              ∞              =      1    very very large number        lim          x      →      ∞        (      e          −      2      x        )  =  0Therefore,      lim          x      →      ∞        (      e          −      2      x        cos  ⁡  x  )  =  0

phoreeldoefk · Accepted Answer

7.       lim          x      →                                    9            π                    2                +              (      e          tan      ⁡      x        )      lim          h      →      0            e          tan      ⁡      (                        9          π                2            +      h      )        =      lim          h      →      0            e          −      cot      ⁡      h                          (  ∵  tan  ⁡  (            9      π        2    +  h  )  =  −  cot  ⁡  h  )  =      lim          h      →      0            e          −      cot      ⁡      h                       (            9      π        2    +  h  ) lies in second quadrant  =      e          −      cot      ⁡      0        =      e          −      ∞        =      1          e              ∞              =      1    very very large number  =0

6.Find the limit lim_(x -> oo) (e^(-2x) cos x) 7.Find the limit lim_(x -> ((9 pi)/(2))^+) e^(tan x)

Open question

Answer & Explanation

New Questions in Differential Calculus