Term Examination - Part 7

Evaluate: lim x² + 3x + 1

• 11
• -11
• 12
• -13

Evaluate: lim of 1/x as x approaches 0

• undefined
• 1
• 0
• no limit

Evaluate: lim of 1/x² as x approaches 0

• 0
• +∞
• 1
• -∞

Evaluate: lim of (x² - 81)/(x - 9) as x approaches 9

• indeterminate
• 0
• undefined
• 18

Evaluate: lim of 2x⁴/(3x⁴ + x³ - x² - x - 1) as x approaches ∞

• +∞
• 2/3
• 0
• indeterminate

Evaluate: lim of (1 - cos x)/x² as x approaches 0

• no limit
• indeterminate
• 0
• 1/2

Evaluate: lim of sin(2/n)/sin(1/n) as x approaches ∞

• 0
• 2
• no limit
• indeterminate

If the radius of the circle increases at the rate of 0.01 inch per second, find the rate of change of the area when the radius is 3 inches long.

• 0.188 in²/s
• 0.440 in²/s
• 0.376 in²/s
• 0.335 in²/s

Find the radius of curvature of the curve y = x⁴ − x² at point (0, 0).

• 1/4
• 3/4
• 1/3
• 1/2

Find the points of inflection of x² + y³ = 2 at the first quadrant.

• (1, 1)
• (-1, -1)
• (1, -1)
• (-1, 1)