External link to Name: _________________________Score: ______ / ______1.Find the indicated sum. Show your work.k = 1, (-1)^k (k + 11) = (-1)^(1) (1…

# Name: _________________________Score: ______ / ______1.Find the indicated sum. Show your work.k = 1, (-1)^k (k + 11) = (-1)^(1) (1…

Name: _________________________ Score: ______ / ______ 1. Find the indicated sum. Show your work. k = 1, (-1)^k (k + 11) = (-1)^(1) (1 + 11)= -1*(12) = -12 k = 2, (-1)^k (k + 11) = (-1)^(2) (2 + 11)= 1*(13) = 13 k = 3, (-1)^k (k + 11) = (-1)^(3) (3 + 11)= -1*(14) = -14 k = 4, (-1)^k (k + […]

External link to Is 0,0,0,… a geometric sequence?

# Is 0,0,0,… a geometric sequence?

Probably, depending on the definition being used. In general, a geometric sequence to be one of the form ##a_n = a_0r^n## where ##a_0## is the initial term and ##r## is the common ratio between terms. In some definitions of a geometric sequence (for example, at the encyclopedia of mathematics) we add a further restriction, dictating that ##r!=0## and ##r!=1##. By those definitions, a sequence such […]

External link to What is the difference between the remainder theorem and the factor theorem?

# What is the difference between the remainder theorem and the factor theorem?

The two theorems are similar, but refer to different things. See explanation. The remainder theorem tells us that for any polynomial ##f(x)##, if you divide it by the binomial ##x-a##, the remainder is equal to the value of ##f(a)##. The factor theorem tells us that if ##a## is a zero of a polynomial ##f(x)##, then ##(x-a)## is a factor of ##f(x)##, and vice-versa. For example, […]

External link to What is the amplitude, period and range for ##f(x)=-2sin(2x)-1## and how do you graph it?

# What is the amplitude, period and range for ##f(x)=-2sin(2x)-1## and how do you graph it?

The amplitude, or (i.e. how far up and down the graph goes) is always the absolute value of the leading coefficient of the function. In this case, it would be -2. Hence, that is your amplitude. This is because the range of sine (and cosine) functions is [1, -1], and by multiplying the entire function by a certain factor, you’re increasing the output by that […]

External link to What does exclamation an point mean in math?

# What does exclamation an point mean in math?

An exclamation point denotes something called a factorial. The formal definition of ##n!## (n factorial) is the product of all the natural numbers less than or equal to ##n##. In math symbols: ##n! = n*(n-1)*(n-2)…## Trust me, it’s less confusing than it sounds. Say you wanted to find ##5!##. You just multiply all the numbers less than or equal to ##5## until you get to […]

External link to How do I find the real zeros of a polynomial function on a graphing calculator?

# How do I find the real zeros of a polynomial function on a graphing calculator?

If you are using a TI-83 or TI-84, then you first graph the function by going into Y= and entering the part after the f(x) or y= after Y1. Now you just need to hit the “graph” key, and you should see a nice graph laid out there. Now what you are looking for are the zeroes. These are the points where the graph intersects […]

External link to How does instantaneous rate of change differ from average rate of change?

# How does instantaneous rate of change differ from average rate of change?

Instantaneous rate of change is measured at one precise point, whilst average rate of change uses two points to average the slope between those two points. In the tangent method, a line is drawn against the function that is the same angle or steepness of the function at that point. This is usually done by eye and is hence subjective and inaccurate compared to calculations […]

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