📈 Choose Your Calculus Practice Area
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🔍 Limits Practice
Find: \lim_{x \to 2} (x^2 + 3x - 2)
Limit =
Hint: Direct substitution: (2² + 3×2 - 2) = ?
Find: \lim_{x \to 0} \frac{\sin x}{x}
Limit =
Hint: This is a fundamental trigonometric limit
Find: \lim_{x \to \infty} \frac{2x^2 + 3x - 1}{x^2 + 1}
Limit =
Hint: Divide numerator and denominator by x²
📊 Derivatives Practice
Find: \frac{d}{dx}[x^3]
Derivative =
Hint: Power rule: d/dx[x^n] = nx^(n-1)
Find: \frac{d}{dx}[\sin x]
Derivative =
Hint: Derivative of sin(x) is cos(x)
Find: \frac{d}{dx}[e^x]
Derivative =
Hint: Derivative of e^x is itself
Find: \frac{d}{dx}[x^2 \sin x]
Derivative =
Hint: Product rule: d/dx[uv] = u'v + uv'
Find f'(2) for: f(x) = x^3 - 2x + 1
f'(2) =
Hint: First find f'(x), then evaluate at x=2
🚀 Applications of Derivatives
Find critical points: f(x) = x^3 - 3x^2 + 1
Critical points:
Hint: Find where f'(x) = 0
A ball is thrown upward with velocity 20 m/s. Find max height.
Max height =
Hint: Use v(t) = 20 - 9.8t, find when v(t) = 0
Find instantaneous rate of change: f(x) = x^2 at x = 3
Slope =
Hint: Find f'(3)
∫ Integrals Practice
Find: \int x^2 \, dx
∫x² dx =
Hint: Power rule: ∫x^n dx = x^(n+1)/(n+1) + C
Find: \int \cos x \, dx
∫cos x dx =
Hint: Integral of cos(x) is sin(x)
Find definite integral: \int_0^1 x^2 \, dx
∫₁₀ x² dx =
Hint: [x³/3] from 0 to 1
Find area under curve: y = x^2 from x=0 to x=2
Area =
Hint: ∫₂₀ x² dx
∑ Series Practice
Find sum of first 5 terms: 1 + 2 + 3 + 4 + 5
Sum =
Hint: Use formula n(n+1)/2
Is this geometric series convergent? \sum \frac{1}{2^n}
Hint: |r| = 1/2 < 1, so converges
Find sum: \sum_{n=1}^{\infty} \frac{1}{2^n}
Sum =
Hint: Geometric series with r = 1/2
🎭 Mixed Calculus Review
Evaluate: \lim_{x \to 0} \frac{e^x - 1}{x}
Limit =
Hint: This is a derivative definition limit
Find: \frac{d}{dx}[\ln x]
Derivative =
Hint: Derivative of ln(x) is 1/x
Evaluate: \int_0^{\pi/2} \cos x \, dx
Integral =
Hint: [sin x] from 0 to π/2
📊 Interactive Function Grapher
📊 Your Calculus Practice Summary
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