Answered: Find the lengths of the curves in…

Math

Calculus

Find the lengths of the curves in Exercises 13–14. 13. y = x^1/2 - (1/3)x^3/2, 1<=x<= 4 14. x = y2/3, 1<= y <= 8

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 44E

See similar textbooks

Related questions

Q: 8. Determine the equation of the tangent line to the graph of the lemniscate: 2(x2 + y2)2 = 25(x² –…

Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: Find the equation of a curve passing thorugh the point (0,2) and having slope x +ex-sinhx at any…

Q: What is the value of the slope of the tangent line to the curve *y+y<=5 passing through the point…

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find: Equation of tangent and normal to the curve at point…

Q: # 3 Find the slope of the tangent line to the curve -3x²-3xy + ly = 33 at the point (- 2, 3).…

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: Find the equation of the tangent plane to the graph of 5y f(x, y) = at the point (9, –1). (Use…

A: The equation of the tangent plane at point (x1, y1, z1) is z-z1=∂z∂x(x1, y1, z1)(x-x1)+∂z∂y(x1, y1,…

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

Q: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

A: The given equation of curve is. We have to find the orthogonal trajectories of family of curve.…

Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

Q: 6. Find the tangent line and normal line to curve y = x3 - 3x2 - 2 at point (1, -4)?

Q: Find equations of the tangent line and normal line to the curve y = 5x-32T at = 4. %3D

A: This question is based on straight line.

Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: Find the equation of the tangent line to the curve y = rVI at the point (4, 8). %3D

A: We have to find the equation of tangent

Q: The slope of the tangent line to the curve y 4 at the point (4, 1) is: - The equation of this…

A: The slope of tangent to any curve is determined by the derivative . So, slope of the tangent…

Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

Q: 3 at the point 7, 3 is: The slope of the tangent line to the curve y %3D

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

Q: is the tangent line to y= 1/2arctan(1/5x) at the point (5,π/8)?

A: Answer and explanation is given below

Q: 9 Find the length of the segment 16 between the lines. y- 1-x + arcsinx of the curve -0, x

Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3, 1≤y≤9 Differentiating with respect to y, we get…

Q: Let y=4x4 + x. At what point is the tangent line to the graph perpendicular to the linet tangent to…

A: if line L1 having slope m1 and line L2 having slope m2 are perpendicular then m1m2=-1

Q: 16. Determine the horizontal tangents on the curve y = 2x'-18x.

Q: Find the equation of tangent line to the curve y = 2 - x 2 (7, ²/7). at the point (7, Express the…

A: The objective is to find the equation of tangent line.

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: parametrically

Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Describe the tangent line at an arbitrary point on the “curve” y = 2x + 8.

Q: the length of the curve y = coshx 1<= x <=2 is sish (2) - sinh(1) Select one: True False

Q: 4. Center at (-4,9), tangent to the x-axis 5. Center at (-4,9), tangent to the y-axis

A: In this question we have to find the equation of the circle tangent to the x-axis and y-axis.

Q: What point on the curve y = x is closest to the point (5, 0)?

Q: Make the curve y = ax4 + bx3 + cx2 + dx + e pass through the points (0,3) and (-2,7) and at (1,4)…

A: The curve y=ax4+bx3+cx2+dx+e

Q: Find an equation of the tangent line to the graph of y = arcsin(2x) at the point 2/2 4

Q: .3 The curve y3Dx+ x*-x has two horizontal tangents. Find the distance between these two horizontal…

Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: Find the length of curve along y = x² from (0,0) into (2,4).

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

Find the lengths of the curves in Exercises 13–14.

13. y = x^1/2 - (1/3)x^3/2, 1<=x<= 4

14. x = y2/3, 1<= y <= 8

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Integration$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Exercises 123–126: Predict the number of tick marks on the positive x-axis and the positive y-axis. Then show the viewing rectangle on your graphing calculator. 123. Standard viewing rectangle 124. [-4.7, 4.7, 1] by [-3.1, 3.1, 1] 125. (0, 100, 10] by [-50, 50, 10] 126. [-30, 30, 5] by (-20, 20, 5]
An object moves on a horizontal coordinate line. Its directed distance s from the origin at theend of t seconds is t^3 − 6t^2 + 9t feet. A. When is its speed increasing?
Is it possible to get a example which shows this applied to a model
Sec6.4:#43
Find the shortest distance from the point (2, 0) to the curve (image attached)
Find the point on the line y=2x that is closest to the point (5,2)
Differentiate the given functions 1)y=-2 2)y=x^7/3 3)y=x^3.7 4)y=pir^2
9. A basketball is thrown from a height of 4 feet so that its path is modeled by the function fx) = -0.03x² + 1.3x +4. If the exact same shot is taken from a balcony that is 12 feet above where the original shooter was standing, how far away will the ball hit the ground? What is the equation that models this shot? %3D
8,9 reflected over x-axis and y-axis
Find the lengths of the curves in Exercises 1– 2. If you have a grapher, you may want to graph these curves to see what they look like. 1- y = (1/3)(x² + 2)³/2 from x = 0 to x = 3 2- y = x³/2_from x = 0 to x = 4
A model for the men’s 100-meter freestyle record times in seconds is given by y = (38,504.4888 + 44.37530536x^2)/(1 + x + x^2) where x = 0 represents 1900. The model and the data points are shown in the graph below. Use this model to predict a reasonable record for a man to swim 100 meters in the year 2000. Explain how you determined your answer.
A model for the men’s 100-meter freestyle record times in seconds is given by y=(38,504.4888 + 44.37530536x^2)/(1+x+x^2) where x = 0 represents 1900. The model and the data points are shown in the graph below. Use this model to predict a reasonable record for a man to swim 100 meters in the year 2000. Explain how you determined your answer.