Prove the tangent line existsHow would one prove that the tangent line at 4 exists on the function f ( x ) = 1 x + x using the formula: m = lim x → 0 1 4 + h + 4 + h − 9 4 h I can't wrap my head around this one :/.Thanks in advance.

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Prove the tangent line existsHow would one prove that the tangent line at   4 exists on the function   f  (  x  )  =      1    x    +      x   using the formula:  m  =      lim          x      →      0                          1                  4          +          h                    +              4        +        h            −              9        4              h  I can&#039;t wrap my head around this one :/.Thanks in advance.

Mateo Tate · Accepted Answer

lim          h      →      0                          1                  4          +          h                    +              4        +        h            −              9        4              h    =      lim          h      →                          1                  4          +          h                    −              1        4              h    +      lim          h      →      0                          4        +        h            −      2        h    =  =      lim          h      →                  −      h              4      h      (      4      +      h      )        +      lim          h      →      0            h          h      (              4        +        h            +      2      )        =  −      1    16    +      1    4    =      3    16

Prove the tangent line exists How would one prove that the tangent line at 4 exists on the function f(x) = 1/x+ sqrt(x) using the formula: m=lim_(x-> 0)((1)/(4+h)+sqrt(4+h) - (9)/(4))/(h) I can't wrap my head around this one :/.

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