Question

\( \infty \) 1. \( \int(1-4 x) e^{-x} d x \) 0 2. \( \int_{1}^{e} \frac{1}{x \ln x} d x \) 3. \( \int_{1}^{3} \frac{1-x}{x^{2}+x-6} d x \) 4. Find the equation of the tangent line to the parametric curve \( x=\theta+\cos \theta, y=1+\sin \theta ; \theta=\pi / 6 \). 5. Find the coordinate of the points on the cardioid \( r=1-\cos \theta \) at which there is a horizontal tangent line, a vertical tangent line, or a singular point. 6. Sketch the graph and determine the arc length of the polar curve \( r=2+2 \sin \theta \).

          \( \infty \)
1. \( \int(1-4 x) e^{-x} d x \)
0
2. \( \int_{1}^{e} \frac{1}{x \ln x} d x \)
3. \( \int_{1}^{3} \frac{1-x}{x^{2}+x-6} d x \)
4. Find the equation of the tangent line to the parametric curve \( x=\theta+\cos \theta, y=1+\sin \theta ; \theta=\pi / 6 \).
5. Find the coordinate of the points on the cardioid \( r=1-\cos \theta \) at which there is a horizontal tangent line, a vertical tangent line, or a singular point.
6. Sketch the graph and determine the arc length of the polar curve \( r=2+2 \sin \theta \).

∞
1. ∫(1-4 x) e^-x d x
0
2. ∫1^e(1)/(x ln x) d x
3. ∫1^3(1-x)/(x^2+x-6) d x
4. Find the equation of the tangent line to the parametric curve x=θ+cosθ, y=1+sinθ ; θ=π / 6.
5. Find the coordinate of the points on the cardioid r=1-cosθ at which there is a horizontal tangent line, a vertical tangent line, or a singular point.
6. Sketch the graph and determine the arc length of the polar curve r=2+2 sinθ.

Added by Christopher P.

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