The point P(0.333333333333333,6) lies on the curve y = 2/x . Let Q be the point (x,2/x). a.) Find the slope of the secant line PQ for the following values of x. If x = 0.433333333333333, the slope of PQ is: ---- If x = 0.343333333333333, the slope of PQ is:---- If x = 0.233333333333333, the slope of PQ is: --- If x = 0.323333333333333, the slope of PQ is: --- b.) Based on the above results, guess the slope of the tangent line to the curve at P(0.333333333333333,6).

Q: There are two tangent lines to the curve y %3D x+ 1 that are parallel to the line x - 2y = 2. Find…

A: We first find dy/dx suing quotient rule

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

A:

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: Find the slope of the tangent line for: y = 2x? – 4x

A:

Q: Find the y-intercept of the tangent line to the curve y =x at the point (2,8).

A: We have given, The curve y = x3 and the point (2, 8).

Q: Find the slope of the tangent line to the graph at the given point. 4xcosy +1 = 5 at the point (2,)

A: Solve, as follows: 4xcosy+1=541cosy+x-sinydydx=0dydx=cosyxsiny

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.