- 2.6.1: For the graphs in Exercises 12, list the x-values for which the fun...
- 2.6.2: For the graphs in Exercises 12, list the x-values for which the fun...
- 2.6.3: In Exercises 34, does the function appear to be differentiable on t...
- 2.6.4: In Exercises 34, does the function appear to be differentiable on t...
- 2.6.5: Decide if the functions in 57 are differentiable at x = 0. Try zoom...
- 2.6.6: Decide if the functions in 57 are differentiable at x = 0. Try zoom...
- 2.6.7: Decide if the functions in 57 are differentiable at x = 0. Try zoom...
- 2.6.8: In each of the following cases, sketch the graph of a continuous fu...
- 2.6.9: Look at the graph of f(x)=(x2 + 0.0001)1/2 shown in Figure 2.59. Th...
- 2.6.10: The acceleration due to gravity, g, varies with height above the su...
- 2.6.11: An electric charge, Q, in a circuit is given as a function of time,...
- 2.6.12: A magnetic field, B, is given as a function of the distance, r, fro...
- 2.6.13: A cable is made of an insulating material in the shape of a long, t...
- 2.6.14: Graph the function defined by g(r) = 1 + cos (r/2) for 2 r 2 0 for ...
- 2.6.15: The potential, , of a charge distribution at a point on the y-axis ...
- 2.6.16: Sometimes, odd behavior can be hidden beneath the surface of a rath...
- 2.6.17: A function f that is not differentiable at x = 0 has a graph with a...
- 2.6.18: If f is not differentiable at a point then it is not continuous at ...
- 2.6.19: A continuous function that is not differentiable at x = 2
- 2.6.20: An invertible function that is not differentiable at x = 0.
- 2.6.21: A rational function that has zeros at x = 1 and is not differentiab...
- 2.6.22: There is a function which is continuous on [1, 5] but not different...
- 2.6.23: If a function is differentiable, then it is continuous.
- 2.6.24: If a function is continuous, then it is differentiable.
- 2.6.25: If a function is not continuous, then it is not differentiable
- 2.6.26: If a function is not differentiable, then it is not continuous
- 2.6.27: Which of the following would be a counterexample to the statement: ...
Solutions for Chapter 2.6: DIFFERENTIABILITY
Full solutions for Calculus: Single Variable | 6th Edition
Additive inverse of a real number
The opposite of b , or -b
Complements or complementary angles
Two angles of positive measure whose sum is 90°
See Compounded k times per year.
Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2
a(b + c) = ab + ac and related properties
Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined
An identity involving a trigonometric function of 2u
Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis
Inequality symbol or
An annuity in which deposits are made at the same time interest is posted.
Partial fraction decomposition
See Partial fractions.
See Sequence of partial sums.
An arrangement of elements of a set, in which order is important.
Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,
A function that assigns real-number values to the outcomes in a sample space.
Reflection across the x-axis
x, y and (x,-y) are reflections of each other across the x-axis.
A statistical measure that does not change much in response to outliers.
A set of equations or inequalities.
The scale of the tick marks on the y-axis in a viewing window.