 2.1: The displacement ( in meters) of an object moving in a straight lin...
 2.2: The graph of is shown. State, with reasons, the numbers at which is...
 2.3: Trace or copy the graph of the function. Then sketch a graph of its...
 2.4: Trace or copy the graph of the function. Then sketch a graph of its...
 2.5: The figure shows the graphs of , , and . Identify each curve, and e...
 2.6: Find a function and a number a such that limhl02 h6 64h f aC
 2.7: The total cost of repaying a student loan at an interest rate of r%...
 2.8: The total fertility rate at time t, denoted by , is an estimate of ...
 2.9: Let be the total value of US currency (coins and banknotes) in circ...
 2.10: Find from first principles, that is, directly from the definition o...
 2.11: Find from first principles, that is, directly from the definition o...
 2.12: (a) If , use the definition of a derivative to find . (b) Find the ...
 2.13: Calculate .y x 2 x 3 4 y
 2.14: Calculate .y 1 sx 1 s 5 x3
 2.15: Calculate .y x 2 x 2 sx y
 2.16: Calculate .y tan x 1 cos x
 2.17: Calculate .y x 2 sin x y
 2.18: Calculate .y x 1 x 2 s7
 2.19: Calculate .y t 4 1 t 4 1 y
 2.20: Calculate .y sincos x y
 2.21: Calculate .y tan s1 x
 2.22: Calculate .y 1 sinx sin x y
 2.23: Calculate .xy 4 x 2 y x 3y y
 2.24: Calculate .y sec1 x 2 x
 2.25: Calculate .sec 2 1 tan 2
 2.26: Calculate .cos y sin 2y xy
 2.27: Calculate .y 1 x x
 2.28: Calculate .y 1s
 2.29: Calculate .sinxy x y
 2.30: Calculate .ssin sx 2 y y
 2.31: Calculate .y cot3x 2 5 y
 2.32: Calculate .y x 4 x 4 4 y
 2.33: Calculate .sx cos sx
 2.34: Calculate .y sin mx x
 2.35: Calculate .y tan2 sin x
 2.36: Calculate .x tan y y 1
 2.37: Calculate .y s 5 x tan x
 2.38: Calculate .y x 1x 4 x 2x 3 y s 5 x ta
 2.39: Calculate .y sin(tan s1 x 3 ) y
 2.40: Calculate .y sin2 (cosssin x )
 2.45: Find the limit.lim x l 0 sec x 1 sin x
 2.46: Find the limit.lim t l 0 t 3 tan3 2t
 2.47: Find an equation of the tangent to the curve at the given point. y ...
 2.48: Find an equation of the tangent to the curve at the given point. x ...
 2.49: Find equations of the tangent line and normal line to the curve at ...
 2.50: Find equations of the tangent line and normal line to the curve at ...
 2.51: (a) If , find . (b) Find equations of the tangent lines to the curv...
 2.52: (a) If , , find and . ; (b) Check to see that your answers to part ...
 2.53: At what points on the curve , , is the tangent line horizontal?
 2.54: Find the points on the ellipse where the tangent line has slope 1.
 2.55: Find a parabola that passes through the point and whose tangent lin...
 2.56: How many tangent lines to the curve ) pass through the point ? At w...
 2.57: f x x ax bx c f x f x 1 x a 1 x b 1 x c cos 2x cos2 x sin
 2.58: (a) By differentiating the doubleangle formula obtain the doublea...
 2.59: Suppose that and , where , , , , and . Find (a) and (b) .
 2.60: If and are the functions whose graphs are shown, let , , and . Find...
 2.61: Find in terms of .fx x 2 tx fx
 2.62: Find in terms of .fx tx 2 fx
 2.63: Find in terms of .fx tx2 f x
 2.64: Find in terms of .f x x a tx b fx
 2.65: Find in terms of .fx t tx f x s
 2.66: Find in terms of .f x sin tx f x
 2.67: Find in terms of .f x tsin x f x
 2.68: Find in terms of .f x t(tan sx )
 2.69: Find in terms of and .hx f x tx f x tx hx f x
 2.70: Find in terms of and .hx f x tx hx f
 2.71: Find in terms of and .hx f tsin 4x t x
 2.72: A particle moves along a horizontal line so that its coordinate at ...
 2.73: A particle moves on a vertical line so that its coordinate at time ...
 2.74: The volume of a right circular cone is , where is the radius of the...
 2.75: The mass of part of a wire is kilograms, where is measured in meter...
 2.76: The cost, in dollars, of producing units of a certain commodity is ...
 2.77: The volume of a cube is increasing at a rate of 10 . How fast is th...
 2.78: A paper cup has the shape of a cone with height 10 cm and radius 3 ...
 2.79: A balloon is rising at a constant speed of . A boy is cycling along...
 2.80: A waterskier skis over the ramp shown in the figure at a speed of ....
 2.81: The angle of elevation of the sun is decreasing at a rate of . How ...
 2.82: (a) Find the linear approximation to near 3. (b) Illustrate part (a...
 2.83: (a) Find the linearization of at . State the corresponding linear a...
 2.84: Evaluate if , , and .
 2.85: A window has the shape of a square surmounted by a semi  circle. T...
 2.86: Express the limit as a derivative and evaluate.
 2.87: Express the limit as a derivative and evaluate.
 2.88: Express the limit as a derivative and evaluate.
 2.90: Suppose is a differentiable function such that nd . Show that
 2.91: Find if it is known that ddx f 2x x 2x
 2.92: Show that the length of the portion of any tangent line to the astr...
Solutions for Chapter 2: Calculus, 7th Edition
Full solutions for Calculus,  7th Edition
ISBN: 9780538497817
Solutions for Chapter 2
Get Full SolutionsSince 87 problems in chapter 2 have been answered, more than 6640 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 7. Calculus, was written by and is associated to the ISBN: 9780538497817. Chapter 2 includes 87 full stepbystep solutions.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Center
The central point in a circle, ellipse, hyperbola, or sphere

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Combination
An arrangement of elements of a set, in which order is not important

Commutative properties
a + b = b + a ab = ba

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Endpoint of an interval
A real number that represents one “end” of an interval.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Horizontal shrink or stretch
See Shrink, stretch.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Measure of center
A measure of the typical, middle, or average value for a data set

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

Vertical stretch or shrink
See Stretch, Shrink.

Ymin
The yvalue of the bottom of the viewing window.