Find the equation of the tangent line to the given curve at, Mathematics

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Find the equation of the tangent line to the given curve at

1. For what values of the constants a and b is the function

547_The Function.png

continuous on all real numbers.

2. Use the intermediate value theorem to show that the function f(x) = 3x - sin (x) - 2 has at least one root between 0 and 1

3. Find the equation of the tangent line to the given curve at the given point.

a. y = 9 - 2x² at (2, 1)

b. y = 2 / (1-3x) at (0,2) and at (-1, 0.5)

c. y = 1/ √x at (4, 0.5)

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