Example Problems

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From basic algebra to calculus, word problems to logarithms. Screenshot any problem and get step-by-step explanations that actually teach you.

Linear Equation

3x + 7 = 22

Isolate the variable by subtracting 7 from both sides, then divide by 3 to find x = 5.

Answer: x = 5

Quadratic Equation

x² - 5x + 6 = 0

Factor into (x - 2)(x - 3) = 0, giving two solutions where the parabola crosses the x-axis.

Answer: x = 2 or x = 3

Integral

∫ x² dx

Apply the power rule: increase the exponent by 1 and divide by the new exponent.

Answer: x³/3 + C

Derivative

d/dx(sin(x))

The derivative of sine is one of the fundamental trig derivatives to memorize.

Answer: cos(x)

Word Problem

A train leaves Chicago at 60 mph. Another leaves 2 hours later at 80 mph. When do they meet?

Set up equations using distance = rate × time. Solve for when distances are equal.

Answer: 8 hours after first train

Logarithm

log₂(8)

Ask: 2 to what power equals 8? Since 2³ = 8, the answer is 3.

Answer: 3

Radical Equation

√(x + 5) = 3

Square both sides to eliminate the radical, then solve the resulting linear equation.

Answer: x = 4

Limit

Find the limit: lim(x→0) sin(x)/x

This famous limit equals 1 and is foundational for derivative of sine.

Answer: 1

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