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Introduction to ABC of calculus:

 ABCof calculus is come under calculus-1 category and it deals with pre-calculus problems. So the term pre-calculus is referred as ABC of calculus in which it deals with secondary algebra problems. Pre-calculusis the combined version of secondary algebra and trigonometry. Basically ABC of calculus deals with solving algebra and trigonometry problems. It prepares the students for learning algebra-1 problems and it is also referred as introduction to analysis. The following are example problems which explain the concept of ABC of calculus.


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ABC of calculus example problems:


Example 1:

Solve trigonometric expression.


[Sin
4x - cos 4x] / [sin 2x - cos 2x]

Solution:

Factor the numerator term

[sin
4x - cos 4x] / [sin 2x - cos 2x]

= [sin
2x - cos 2x][sin 2x + cos 2x] / [sin 2x - cos 2x]

Solve it

= [sin
2x + cos 2x]

[Sin 4x - cos 4x] / [sin 2x - cos 2x] = 1

Example 2:

Solve the trigonometric expression.


sin
2x - cos 2x sin 2x

Solution:

Factor sin 2x out, group and simplify

sin
2x - cos 2x sin 2x

= sin
2x (1 - cos 2x)

sin 2x - cos 2x sin 2x
= sin 4x

Example 3:

Determine s(4), t(4) and s(4) / t(4) where functions s and t are defined by

s (y) = 3y - 8 , t (y) = y 2 - 16

Solution:

Evaluate s(4)

s(4) = 3(4) - 8 = 4

Evaluate t(4)

t (4) = 4
2 - 16
= 16 -16 = 0

While calculating s (4) / t(4), t(4) in which the denominator is equal to 0.

s (4) / t (4) = undefined


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ABC of calculus practice problems:


1)      Solve trigonometric expression.

        [Sin 2x - cos 2x] / [sin 4x - cos 4x]

Answer:  1 / [sin 2x + cos 2x] = 1

 2) Determine, s (4), t (4) and s (4) / t (4) where functions s and t are defined by

                s (y) = 4y - 6 , t (y) = y 2 - 25

Answer: s (4) / t (4) = -10/9