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Slope of Tangent Line : It is the next major interpretation of the derivative. The slope of the tangent line to f ( x ) at x = a is f ′ ( a ) . Then the tangent line is given by,
y = f ( a ) + f ′ ( a ) ( x - a )
Example : Determine the tangent line to the given function at z = 3 .
Solution : The derivative is,
Now all that we require is the function value & derivative (for the slope) at z = 3 .
R (3) =√7 m = R′ (3) = 5 /2√ 7
Then the tangent line is,
y = √7 + 5/2√7(z-3)
Example: If c ≠ 0 , evaluate the subsequent integral. Solution Remember that you require converting improper integrals to limits as given, Here, do the integ
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