# What is the equation of the tangent planes to #7x^2-3y^2-z^2+21=0# which passes through the line #7x-6y+9=0#,#z=3#?

See below.

Calliing

and

This last relationship must be true for all

or resuming

In the present case we have

Solving for

and consequently

Attached the surface

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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.

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