Questions from General Calculus

Q: Use a graphing utility to sketch the intersecting graphs of the equations

Use a graphing utility to sketch the intersecting graphs of the equations and show that they are orthogonal. [Two graphs are orthogonal if at their point(s) of intersection, their tangent lines are pe...

Q: Use a graphing utility to sketch the intersecting graphs of the equations

Use a graphing utility to sketch the intersecting graphs of the equations and show that they are orthogonal. [Two graphs are orthogonal if at their point(s) of intersection, their tangent lines are pe...

Q: x3 = 3(y - 1) x(3y

x3 = 3(y - 1) x(3y - 29) = 3 Use a graphing utility to sketch the intersecting graphs of the equations and show that they are orthogonal. [Two graphs are orthogonal if at their point(s) of intersecti...

Q: xy = C, x2 – y2 = k Verify that

xy = C, x2 – y2 = k Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a graphing utility to graph the two families for two values of C and two values of K....

Q: Verify that the two families of curves are orthogonal, where C

Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a graphing utility to graph the two families for two values of C and two values of K. x2 + y2 = C2...

Q: The figure below shows the topographic map carried by a group of

The figure below shows the topographic map carried by a group of hikers. The hikers are in a wooded area on top of the hill shown on the map, and they decide to follow the path of steepest descent (or...

Q: Use the graph to answer the questions. /

Use the graph to answer the questions. Which is greater, the slope of the tangent line at x = -3 3 or the slope of the tangent line at x = -1? Estimate the point(s) where the graph has a vertical ta...

Q: Consider the equation x4 = 4(4x2 – y2)

Consider the equation x4 = 4(4x2 – y2) Use a graphing utility to graph the equation. Find and graph the four tangent lines to the curve for y = 3 Find the exact coordinates of the point of intersecti...

Q: Let L be any tangent line to the curve /

Let L be any tangent line to the curve Show that the sum of the x- and y- intercepts of L is c.

Q: Prove (Theorem 2.3) that / for

Prove (Theorem 2.3) that for the case in which n is a rational number. (Hint: Write y = xp/q in the form yq = xp and differentiate implicitly. Assume that p and q are integers, where q > 0.)