1. For the function(x) = x⁴ determine an approximation for the slope of the tangent to the curve at the point wherea= 0.5. Use, andh = 0.1. Show all your steps.
2. a) For the functionfind an expression for the slope of a tangent at any using. Simplify the expression. This is a function for slope of the function. Then evaluate this expressionby substituting a = 1. Note: What you are doing here is finding the value of the slope of the tangent of f(x)= 1/x² at the point x = 1. b) Determine the equation of this tangent line (in the form y = mx + b) using the slope of the tangent line of f(x) = 1/x²at the point x = 1 or (1,1)
3. A science project studying catapults sent a projectile into the air with an initial velocity of30 m/s. The formula for distance (s) in meters with respect to time in seconds is s(t) = -4.9t²+ 30t. Find the instantaneous rate of change (the velocity function) at any time using.

Determine the instantaneous rate of change (ie. the velocity) at: a) t =2 b)t =5

4. Evaluate the following limits a)limh>0(3+h)333hlimh->0(3+h)3-33h

b) limx>4x2+7x+12x216limx->-4x2+7x+12x2-16

c) limx>2x38x24limx->2x3-8x2-4

d) limx>1x1x21limx->1x-1x2-1

e)limx>0x+77x