1. Consider the piecewise function 2t-t 0st<2 2 - t, 2
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
1 2 and 3. NOT 4
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1. Consider the piecewise function
( 2t – t² 0<t< 2
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2 - t,
2 <t<3
!!
- New
f(t) =
|t – 4,
3 <t< 4
t > 4
5 115
21115
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wt of s
(a) For each of the values of x = 2, 3, and 4, discover whether f(t) is contin-
uous using the continuity test.
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(b) Sketch the graph of f(t) and test the differentiability of the function at
the at the point x = 3.
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2. A company's annual revenues dropped from £450000 in the year 2005 to
£343, 000 in 2008. Assume that the revenue is declining exponentially.
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(a) What is the expected revenue in 2010?
(b) What is the expected revenue in 2014?
VI+t at
3. (a) Find the local linear approximation of the function f(t)
to = 0, and use it to approximate V1.60 and
(b) Graph f and its tangent line at to together, and use the graphs to illus-
trate the relationship between the exact values and the approximations
of V1.60 and V0.50.
175
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4. (a) Determine where f(x) = x4 – 2x3 – x2 – 5 is increasing and decreasing.
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