Evaluate the following limits:
z-+1* x 1
z-++00 3x³ 1
1->-00 3x³ 1
z-++00 3.5 1
z->-00 3r¹ 1
Find a value of K so that the function f(x) is continuous at x = 0 where
@ - = - Calculate lim
Evaluate lim tan(2x)
b Use the definition of derivative to find j'(2) for f(x) = I2 - 3x.
Find the equation of the tangent line of the graph of the function f(x) = x² - 3x at
the point (2,-2). What is the area of the triangle formed by this tangent line and the
Find the equation of the tangent line to the curve y - 2r³ - 3x2 - 3Gx - 82 at its point
(b) Let y(x) be defined implicitly by the equation 1y - r+ 2y. Find y at the point (2,1).
Find the derivatives of the following functions Simplify your answers
In |sec r + tan x)
aresin r + arccos I
Let /(x) = In|(x - 1)(x + 1)(x - 3)].
What is the domain of the function f(x) ?
For what values of x in the domain of
Show that the equation f(x) = 2x³-3x²-36x-82 - 0 has a solution for some x* € (4,5).
Apply Newton's method to this equation with an initial guess To - 4 to find T1 and
evaluate /(I)). Now use To = 5 to find x1 and evaluate f(x1) for this T1. Which one of
these two approximations would you use for x*?
Use 'Hopital's rule to find the following limits:
=-+0 x -sin
Use the 7 step method to sketch the graph of the curve y = 2r³ - 3x2 - 36x - 82.
Find a value of c that satisfies the conclusion of the MVT for f(x) = +2 - x - 6
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