- 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 double-angle formula obtain the double-a...
- 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
An equation that relates variable quantities associated with phenomena being studied
The central point in a circle, ellipse, hyperbola, or sphere
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively
An arrangement of elements of a set, in which order is not important
a + b = b + a ab = ba
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.
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.
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
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.
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.
The y-value of the bottom of the viewing window.