- 4.1: Use the given graph of to find the Riemann sum with six subinterval...
- 4.2: (a) Evaluate the Riemann sum for with four subintervals, taking the...
- 4.3: Evaluate by interpreting it in terms of areas.
- 4.4: Express as a definite integral on the interval and then evaluate th...
- 4.6: (a) Write as a limit of Riemann sums, taking the sample points to b...
- 4.7: The following figure shows the graphs of , and . Identify each grap...
- 4.8: Evaluate: (a
- 4.9: Evaluate the integral
- 4.10: Evaluate the integral
- 4.11: Evaluate the integral
- 4.12: Evaluate the integral
- 4.13: Evaluate the integral
- 4.14: Evaluate the integral
- 4.15: Evaluate the integral
- 4.16: Evaluate the integral
- 4.17: Evaluate the integral
- 4.18: Evaluate the integral
- 4.19: Evaluate the integral
- 4.20: Evaluate the integral
- 4.21: Evaluate the integral
- 4.22: Evaluate the integral
- 4.23: Evaluate the integral
- 4.24: Evaluate the integral
- 4.25: Evaluate the integral
- 4.26: Evaluate the integral
- 4.27: Evaluate the integral
- 4.28: Evaluate the integral
- 4.29: Evaluate the indefinite integral. Illustrate and check that your an...
- 4.30: Evaluate the indefinite integral. Illustrate and check that your an...
- 4.31: Use a graph to give a rough estimate of the area of the region that...
- 4.32: Graph the function and use the graph to guess the value of the inte...
- 4.33: Find the derivative of the function.
- 4.34: Find the derivative of the function.
- 4.35: Find the derivative of the function.
- 4.36: Find the derivative of the function.
- 4.37: Find the derivative of the function.
- 4.38: Find the derivative of the function.
- 4.39: Use Property 8 of integrals to estimate the value of the integral.
- 4.40: Use Property 8 of integrals to estimate the value of the integral
- 4.41: Use the properties of integrals to verify the inequality
- 4.42: Use the properties of integrals to verify the inequality
- 4.43: Use the Midpoint Rule with to approximate
- 4.44: A particle moves along a line with velocity function , where is mea...
- 4.45: Let be the rate at which the worlds oil is consumed, where is measu...
- 4.46: A radar gun was used to record the speed of a runner at the times g...
- 4.47: A population of honeybees increased at a rate of bees per week, whe...
- 4.48: Let Evaluate by interpreting the integral as a difference of areas.
- 4.49: If is continuous and , evaluate .
- 4.50: The Fresnel function was introduced in Section 4.3. Fresnel also us...
- 4.51: If is a continuous function such that for all , find an explicit fo...
- 4.52: Find a function and a value of the constant such that
- 4.53: If is continuous on , show that
- 4.55: If is continuous on , prove that
- 4.56: Evaluate f x f x f a, b 2 y b a fx fx dx fb 2 fa 2 lim hl0 1 h y 2h...
Solutions for Chapter 4: Single Variable Calculus 7th Edition
Full solutions for Single Variable Calculus | 7th Edition
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively
A coordinate plane used to represent the complex numbers. The x-axis of the complex plane is called the real axis and the y-axis is the imaginary axis
Constant of variation
See Power function.
Direction vector for a line
A vector in the direction of a line in three-dimensional space
Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row
The points (x, y, z) in space with x > 0 y > 0, and z > 0.
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>
Imaginary part of a complex number
See Complex number.
A statement that compares two quantities using an inequality symbol
The inverse relation of a one-to-one function.
Line of symmetry
A line over which a graph is the mirror image of itself
A system of linear equations
See Absolute value of a complex number.
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.
Real number line
A horizontal line that represents the set of real numbers.
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator
Solve by substitution
Method for solving systems of linear equations.
Standard form: equation of a circle
(x - h)2 + (y - k2) = r 2
An identity involving a trigonometric function of u + v