For #f(x)=x^2sin(x^3/3)# what is the equation of the tangent line at #x=pi#?
Solution reworked! Tony B
Let Let Let Let '~~~~~~~~~~~~~~~~~~~~~~~~~~~ '~~~~~~~~~~~~~~~~~~~~~~~~~~ '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ So '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Thus At Consider The So This is For reference So Thus the equation of the tangent is
Using :
So
Derived the gradient as -64.6977 to 4 decimal places
Need to establish a point coordinate so that
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So equation (1) becomes
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The equation of the tangent line at x=pi for the function f(x)=x^2sin(x^3/3) is y = -3pi^2 + 3pi(x-pi).
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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.
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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