Home > Calculus > Tangent Line to a Curve

What is the equation of the tangent line of #f(x)=sqrt(x+1) # at #x=0#?

Answer 1

Ezekiel Alexander

# 2y-x-2=0#

We have #f(0)=1#, and

#f^'(x) = 1/(2sqrt(x+1))#

and thus

#f^'(0) = 1/2#

So, the required tangent is a straight line with slope #1/2#, passing through #(0,1)#

The equation is present.

#y-1 = 1/2(x-0) implies 2y-x-2=0#

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

Answer 2

Evelyn Agard

The equation of the tangent line of f(x)=sqrt(x+1) at x=0 is y = 1/2x + 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.

Trending questions

Not the question you need?

HIX Tutor

Solve ANY homework problem with a smart AI

98% accuracy study help
Covers math, physics, chemistry, biology, and more
Step-by-step, in-depth guides
Readily available 24/7