Calculus: Early Transcendental Functions 6th Edition solutions

Calculus: Early Transcendental Functions 6
A force of 180 pounds acts on the bracket shown in the figure. (a) Determine the vector \(\overrightarrow{A B}\) and the vector F representing the force. (F will be in terms of \(\theta\).) (b) Find the magnitude of the moment about A by evaluating \(\|\overrightarrow{A B} \times \mathbf{F}\|

Calculus: Early Transcendental Functions 6
In Exercises 4760, find the indefinite integral. \(\int \frac{x+4}{\left(x^{2}+8 x-7\right)^{2}} d x\) Text Transcription: \int \frac x+4 (x^{2}+8 x-7)^2 d x

Calculus: Early Transcendental Functions 6
A wire 24 inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of \(x). (a) Write the area of the rectangle as a function of \(x\). (b) Determine the domain of the function and use a graphing utility to graph the function over that domain. (c

Calculus: Early Transcendental Functions 6
Matching In Exercises 1-6, match the function with one of the graphs [(a), (b), (c), (d), (e), or (f)] using horizontal asymptotes as an aid. \(f(x)=\frac{2 x}{\sqrt{x^{2}+2}}\) Text Transcription: f(x)=2x/sqrt x^2+2

Calculus: Early Transcendental Functions 6
Secant Lines Consider the function \(f(x)=\sqrt{x}\) And the point P(4, 2) on the graph of f. (a) Graph f and the secant lines passing through P(4, 2) and Q(x,.f(x)) for x-values of 1, 3, and 5. (b) Find the slope of each secant line. (c) Use the results of part (b) to estimate t

Calculus: Early Transcendental Functions 6
Estimating Slope In Exercises 1 and 2, estimate the slope of the graph at the points \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) Text Transcription: (x_1, y_1) and (x_2, y_ 2)

Calculus: Early Transcendental Functions 6
Finding a Value In Exercises 6570, find k such that the line is tangent to the graph of the function. Function Line \(f(x)=k x^{4}\) \(y=4 x-1\)

Calculus: Early Transcendental Functions 6
Finding a Particular Solution In Exercises 5-10,find a particular solution of the differential equation. y + 7y + 12y = 3x + 1

Calculus: Early Transcendental Functions 6
In Exercises 1-6, evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \(\sinh ^{-1} 0\) (b) \(\tanh ^{-1} 0\) Text Transcription: sinh ^-1 0 tanh ^-1 0

Calculus: Early Transcendental Functions 6
Finding Arc Length In Exercises 3-16,find the arc length of the graph of the function over the indicated interval. \(y=\ln (\sin x), \quad\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\) Text Transcription: y=ln(sin x), [

Calculus: Early Transcendental Functions 6
In Exercises 14, (a) find the component form of the vector v and (b) sketch the vector with its initial point at the origin.

Calculus: Early Transcendental Functions 6
Solving an Exact Differential Equation In Exercises 3-8, determine whether the differential equation is exact. If it is,find the general solution. \((10 x+8 y+2) d x+(8 x+5 y+2) d y=0\) Text Transcription: (10 x+8 y+

Calculus: Early Transcendental Functions 6
Using Related Rates In Exercises 14, assume that x and y are both differentiable functions of t and find the required values of \(d y / d t \text { and } d x / d\). Equation Find Given \(y=\sqrt{x}\) (a) \(\frac{d y}{d t} \tex

Calculus: Early Transcendental Functions 6
In Exercises 14, find any intercepts. y = 5x - 8

Calculus: Early Transcendental Functions 6
Angular Rate of Change An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider \(\theta\) and x as shown in the figure. (a) Write \(\theta\) as a function of x. (b) The speed of the plane is 400 miles per hour. Find \(d \theta / d t\) when x = 10 mil

Calculus: Early Transcendental Functions 6
Finding a Particular Solution In Exercises 5-10,find a particular solution of the differential equation. y - y - 6y = 4

Calculus: Early Transcendental Functions 6
Finding the Arc Length of a Plane Curve In Exercises 1-6,sketch the plane curve and find its length over the given interval. \(\mathbf{r}(t)=t^{3} \mathbf{i}+t^{2} \mathbf{j}, \quad[0,1]\) Text Transcription: r(t)=t^3

Calculus: Early Transcendental Functions 6
In Exercises 1-4, use the given values to write the predator-prey equations dx/dt = ax - bxy and dy/dt = -my + nxy. Then find the values of x and y for which dx/dt = dy/dt = 0. a = 1.2, b = 0.04, m = 1.2, n = 0.02

Calculus: Early Transcendental Functions 6
Limits and Continuity In Exercises 1-6, use the graph to determine the limit, and discuss the continuity of the function. (a) \(\lim _{x \rightarrow c^{+}} f(x)\) (b) \(\lim _{x \rightarrow c^{-}} f(x)\) (c) \(\lim _{x \rightarrow c} f(x)\) lim_x rightarrow c f(x)

Calculus: Early Transcendental Functions 6
In Exercises 14, estimate the slope of the line from its graph. To print an enlarged copy of the graph, go to MathGraphs.com.