Home > Calculus > Tangent Line to a Curve

What is the equation of the line tangent to # f(x)=x + cos (x)# at # x=0 #?

Answer 1

#x-y+1=0#. Interestingly, this is the bounding tangent for the whole periodic wave, from above. The parallel one below is x-y-1=0. See Socratic graphs.

Thus, the point of contact P of the tangent is (0, 1) at x = 0, f = 1.

At P, the tangent's slope is f' = 1+sin x = 1.

The tangent equation at P(0, 1) is now

#y-1=1(x-0)#, giving

#x-y+1=0#

graph{(x+cosx-y)(x-y+1.05)(x^2+(y-1)^2-.01)=0 [-5, 5, -2.5, 2.5]} graph{(x+cosx-y)(x-y+1.05)(x-y-1)(x^2+(y-1)^2-.01)=0 [-30, 30 -15, 15]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Adkins

The equation of the line tangent to f(x)=x + cos(x) at x=0 is y = 1.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

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.