Question

Using limit to find the equation of the tangent line to the curve y = f(t)=2t^3+3t at the point Q(1,5)

Answer 1

The equation of a tangent line is given by

where : m = slope of tangent line

: C= Y-intercept of the line

Using limits , the slope of tangent line is detremined by

where ' a' is any x coordinate through which the tangent line opasss

Here lines passes through (1,5) that means a = 1

Therefore m= can be written as,

  

• If we directly apply t =1

Sice it is the form we can use L.hospital rule

• L . hospital rule states that if we apply the limit and the function gives a value of form

we can take the derivative of numerator and denominator seperately and apply the limit

EQUATIONS USED

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The equation tangent line is

We still need to find Y-intercept C

we know that tangent line asses through (1 , 5) which means when x = 1 , y = 5

Therefore final equation of tangent line is