Graphing
a.) Draw an accurate graph of y=x2 over the x=[-2,2].
b.)Find the equation of the secant line over the interval x=[0,2]. Accurately sketch this on the graph above.
c.)Fine the equation of the tangent line at x=1. Accurately sketch this on the graph above.
d.)State the average rate of change over the interval x=[0,2].
e.)State the instantaneous rate of change at x=1
Homework Answers
please answer the following parts. thank you in advance Let's consider the problem that has given rise to the...
please answer the following parts. thank you in advance
Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of-snx. (5) 1. On graph paper, sketch the graph of y-sin and draw a tangent line at...
please answer all the following parts neatly. thank you Let's consider the problem that has given rise t...
please answer all the following parts neatly. thank you
Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of f)-sinx (5) . On graph paper, sketch the graph of -sinx and draw a tangent line...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the f...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. b) Find the number c that satisfies the conclusion of the meat value theorem on the given interval. (c) Sketch a neat, clearly labeled graph with the function, the secant line that goes through the end points, and the tangent line at (c./(c)) all on the same coordinate grid (d) Are...
4. In class, we used both graphical and table methods to develop the idea that we...
4. In class, we used both graphical and table methods to develop the idea that we can take a series of secant lines (lines that pass through two points of a function) and use them to approximate a tangent line. While the secant lines give us an approximate change, the tangent line gives us an instantaneous rate of change or the slopel/steepness of a graph at a single point. Do you this method always works? Does every point on every...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). Suppose (2) = - 2 (7+h)-(7) 1-10) lim A0 (0)-0 0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the slope of the tangent line to the...
The tangent line to the graph of f(x) at x 1 is shown. On the tangent...
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
2 The mass M in grams of undissolved sugar left in a teacup after t seconds is given by M = 10.5 - 0.4ť . a) When w...
2 The mass M in grams of undissolved sugar left in a teacup after t seconds is given by M = 10.5 - 0.4ť . a) When will all the sugar dissolve? (2 marks) Find the average rate of change in the interval 0 ts1. (1 mark) b) Draw on graphing paper a graph of M with respect to t and use the secant method to approximate the instantaneous rate of change at t 2 seconds. (3 marks) c)
2...
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of...
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of the function and sketch a graph of its derivative directly beneath. a) b) c) 0 any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x-3)2 at P-(1,...
A function and an interval of its independent variable are given. The endpoints of the interval...
A function and an interval of its independent variable are given. The endpoints of the interval are associated with the points P and Q on the graph of the function. Answer parts a and b The volume V of a gas in cubic centimeters is given by Vwhere p is the pressure in atmospheres and 0.5 sps2 a. Sketch a graph of the function and the secant line through P and Q b. Find the slope of the secant line...
8 The Newton-Raphson method. This is a technique which was developed independently approximately 300 years ago by two Isaac Newton and Joseph Raphson. This is an iterative (repetitive) technique whi...
8 The Newton-Raphson method. This is a technique which was developed independently approximately 300 years ago by two Isaac Newton and Joseph Raphson. This is an iterative (repetitive) technique which produces successively better approximations for the roots (or zeros) of a real function. Using this technique, if we cannot solve an equation, we can find a very accurate approximation to its roots. Say we cannot solve some equation f(x)- 0. We can investigate its roots by drawing the graph of...
please answer the following parts. thank you in advance
Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of-snx. (5) 1. On graph paper, sketch the graph of y-sin and draw a tangent line at...
please answer all the following parts neatly. thank you
Let's consider the problem that has given rise to the branch of calculus called differential calculus: the tangent problem. This problem relates to finding the slope of the tangent line to a curve at a given point. To understand how this is done we are going to consider the point (0,0) on the graph of f)-sinx (5) . On graph paper, sketch the graph of -sinx and draw a tangent line...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. b) Find the number c that satisfies the conclusion of the meat value theorem on the given interval. (c) Sketch a neat, clearly labeled graph with the function, the secant line that goes through the end points, and the tangent line at (c./(c)) all on the same coordinate grid (d) Are...
4. In class, we used both graphical and table methods to develop the idea that we can take a series of secant lines (lines that pass through two points of a function) and use them to approximate a tangent line. While the secant lines give us an approximate change, the tangent line gives us an instantaneous rate of change or the slopel/steepness of a graph at a single point. Do you this method always works? Does every point on every...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). Suppose (2) = - 2 (7+h)-(7) 1-10) lim A0 (0)-0 0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the slope of the tangent line to the...
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
2 The mass M in grams of undissolved sugar left in a teacup after t seconds is given by M = 10.5 - 0.4ť . a) When will all the sugar dissolve? (2 marks) Find the average rate of change in the interval 0 ts1. (1 mark) b) Draw on graphing paper a graph of M with respect to t and use the secant method to approximate the instantaneous rate of change at t 2 seconds. (3 marks) c)
2...
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of the function and sketch a graph of its derivative directly beneath. a) b) c) 0 any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x-3)2 at P-(1,...
A function and an interval of its independent variable are given. The endpoints of the interval are associated with the points P and Q on the graph of the function. Answer parts a and b The volume V of a gas in cubic centimeters is given by Vwhere p is the pressure in atmospheres and 0.5 sps2 a. Sketch a graph of the function and the secant line through P and Q b. Find the slope of the secant line...
8 The Newton-Raphson method. This is a technique which was developed independently approximately 300 years ago by two Isaac Newton and Joseph Raphson. This is an iterative (repetitive) technique which produces successively better approximations for the roots (or zeros) of a real function. Using this technique, if we cannot solve an equation, we can find a very accurate approximation to its roots. Say we cannot solve some equation f(x)- 0. We can investigate its roots by drawing the graph of...
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