# What is the equation of the line tangent to # f(x)=x/secx # at # x=pi/3#?

Since we are talking about a tangent this means we'll want to find the gradient at that point.

Using product rule:

Using point-gradient formula:

This gives you:

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The equation of the line tangent to f(x) = x/sec(x) at x = pi/3 is y = (pi/3) * sec(pi/3) - (pi/3) * tan(pi/3) + (x - pi/3) * sec(pi/3) * tan(pi/3).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the instantaneous velocity of an object moving in accordance to # f(t)= (2sin(2t+pi),tcos2t) # at # t=pi/3 #?
- What is the equation of the line normal to #f(x)=x^2+8x - 12# at #x=3#?
- What is the equation of the tangent line of #f(x) =x^2-x+4# at #x=2#?
- What is the equation of the line normal to #f(x)=3x^2 -5x +1 # at #x=-3#?
- What is the equation of the line that is normal to #f(x)= (2x-2)e^(2x-2) # at # x= 1 #?

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