Weekly Problem Set 2 1. Consider the function Ex)=x". [10 pts] a) Write out the limit...
Homework Set 6: Problem 11 Previous Problem Problem List Next Problem (1 point) Consider the function y = g(x) = -2? +52 +2. (a) Use the limit definition to compute a formula for y=g'(x). y= (b) Determine the slope of the tangent line to y=9(x) at the value x = 3. slope = (c) Compute g(3) 9(3) = (d) The equation for the tangent line to y = 9(2) at the point (3,9(3)), written in point-slope form, is (1- Fill...
Problem 4. (10 pts) Consider the function g(x) = 2x3 – 4x2 + 8. (a) Give the equation of the tangent line centered at x = 2. (b) Approximate g(2.1) using the tangent line. (c) What is the relative error from the approximation in part (c)?
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
Use the fact that the derivative of the function g(x) = /x is g'(x) = 2/x to find the equation of the tangent line to the graph of g(x) at the point x = 1. %3D The equation of the tangent line is y = (Simplify your answer.) is f'(x) = Use the fact that the derivative of the function f(x) = to find the equation of the tangent line to the graph of f(x) at the point x= -...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
2. Use the ε - δ definition for the limit to prove that limx→-2 (4x - 3) = -113. Use the limit definition of the derivative to find the derivative of the function f(x) = √(4x + 1)4. Find the equation of the tangent line to the curve ve y = (1 + 2x) 10 at the point (-1,1).
Consider the following function. f(x) = -½x2 – 3x + 1 Find the slope and an equation of the tangent line to the graph of the function at the point (-2,5). Slope: m= Equation: y = (Enter equation in slope-intercept form, i.e.y = mx + b)
Consider the cubic function y2r3 13z2 -13 -10. (a) Find the local maximum and minumum for the curve (to two decimals), and sketch a graph for the cubic function for-13r<6. (b) Find the equation for the tangent to the curve at the point where x = 0· Sketch the graph for the tangent on the same coordinate system as the cubic function.
Consider the cubic function y2r3 13z2 -13 -10. (a) Find the local maximum and minumum for the curve...
Problem 4 (20 PTS) For the given function: 2(,y) = re (1) (8 PTS) Determine 2x , zy, Zry, and Zyz. (2) (4 PTS) State whether the conclusion of Clairaut's theorem holds for z(x, y) and explain your answer. (3) (8 PTS) Determine and write down the equation of the tangent plane to the surface : at the point P(1,0,1). Give the equation in standard form, i.e. in the form Ax+By+C2 = D.