Thomas' Calculus: Fourteenth Edition Overview | Verified Answers 100%

Thomas - AP Calculus| Verified Answers 100%


sin(0π) - ANSWER 0
sin(π/6) - ANSWER 1/2
sin(π/4) - ANSWER √(2)/2
sin(π/3) - ANSWER √(3)/2
sin(π/2) - ANSWER 1
sin(π) - ANSWER 0
sin(3π/2) - ANSWER -1
sin(2π) - ANSWER 0
cos(0π) - ANSWER 1
cos(π/6) - ANSWER √(3)/2
cos(π/4) - ANSWER √(2)/2
cos(π/3) - ANSWER 1/2
cos(π/2) - ANSWER 0
cos(π) - ANSWER -1
cos(3π/2) - ANSWER 0
cos(2π) - ANSWER 1
tan(θ)
- represented by sin and/or cos. - ANSWER sin(θ)/cos(θ)
cot(θ)
- represented by sin and/or cos. - ANSWER cos(θ)/sin(θ)
csc(θ)
- represented by sin and/or cos. - ANSWER 1/sin(θ)
sec(θ)
- represented by sin and/or cos. - ANSWER 1/cos(θ)
y = sin(x) - ANSWER Match the Graph
y = cos(x) - ANSWER Match the Graph
y = tan(x) - ANSWER Match the Graph
y = sec(x) - ANSWER Match the Graph
y = 1/x - ANSWER Match the Graph
(Asymptote at y = 0)
y = √x - ANSWER Match the Graph
y = √(1 - x²) - ANSWER Match the Graph
y = |x| - ANSWER Match the Graph
y = ln(x) - ANSWER Match the Graph
(Asymptote at x = 0)
y = e^x - ANSWER Match the Graph
(Asymptote at y = 0)
Definition of an EVEN FUNCTION: - ANSWER • Symmetric with respect to
the y-axis.
• f(-x) = f(x)
• y = cos(x), |x|, x² are examples



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, Definition of an ODD FUNCTION: - ANSWER • Symmetric with respect to
the origin.
• f(-x) = -f(x)
• y = x³, sin(x), tan(x) are examples
What is/are the formula(s) for the AREA of a triangle? - ANSWER •A=
(1/2)*b*h
• A = (1/2)*a*b*sin(C)
What is/are the formula(s) for the AREA of a circle? - ANSWER • A = πr²
What is/are the formula(s) for the CIRCUMFERENCE of a circle? - ANSWER
• C = 2πr
What is/are the formula(s) for the VOLUME of a cylinder? - ANSWER •V=
πr²h
What is the formula for the VOLUME of a cone? - ANSWER • V = (1/3)*πr²h
What is/are the formula(s) for the VOLUME of a sphere? - ANSWER •V=
(4/3)*πr³
What is/are the formula(s) for the SURFACE AREA of a sphere? - ANSWER
• A = 4πr²
What is the point-slope form of an equation? - ANSWER • y - y₁ = m(x - x₁)
lim x→0 [sin(x) / x] - ANSWER 1
lim x→0 ([1 - cos(x)] / x) - ANSWER 0
Definition of a TANGENT LINE: - ANSWER The line through a point on a
curve with slope equal to the slope of the curve at that point.
Definition of a SECANT LINE: - ANSWER The line connecting two points on
a curve.
Definition of a NORMAL LINE: - ANSWER The line perpendicular to the
tangent line at the point of tangency.
Definition of f(x) continuity at x = c: - ANSWER • f(c) exists
• lim x→c ( f(x) ) exists
• lim x→c ( f(x) ) = f(c)
Definition of the derivative using limits, f'(x) = : - ANSWER lim ∆x→0 [ (f(x +
∆x) - f(x)) / ∆x ]
Definition of the derivative using limits, alternate, f'(c) =: - ANSWER lim x→c
[ (f(x) - f(c)) / (x - c) ]
Three things f'(x) tells you about a function: - ANSWER • Slope of a curve at
a point
• Slope of the tangent line
• Instantaneous rate of change
Definition of Average Rate of Change, (∆y/∆x) =: - ANSWER (f(b) - f(a)) / (b -
a)
Power Rule for Derivatives / (d/dx [xⁿ] =) - ANSWER nxⁿ⁻¹
Product Rule for Derivatives / (d/dx [f(x) * g(x)]) - ANSWER f'(x)*g(x) +
f(x)*g'(x)
OR 1 d2 + 2 d1
Quotient Rule for Derivatives / (d/dx [f(x)/g(x)]) - ANSWER [f'(x)*g(x) -
f(x)*g'(x)] / [g(x)]²
OR lo dhi - hi dlo over lolo

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