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- Question 1 of 26
##### 1. Question

1 point(s)Category: K/U1. Determine \( \lim_{x\to -2} \left(3x+x^2 \right) \).

CorrectIncorrect - Question 2 of 26
##### 2. Question

1 point(s)Category: K/U2. Determine \( \lim_{x \to -2} f(x), \: \textrm{where} \: f(x)= \begin{cases} 3, & \text{if} \; x = -2 \\ -3, & \text{if} \; x \neq -2 \end{cases} \)

CorrectIncorrect - Question 3 of 26
##### 3. Question

1 point(s)Category: K/U3. Determine an expression, in simplified form, for the slope of the secant

*PQ*with \( P(1, 2) \) and \( Q(1 + h, f(1 + h)) \), where \( f(x) = 2x^2 \).CorrectIncorrect - Question 4 of 26
##### 4. Question

1 point(s)Category: K/U4. Consider the following graph of a function \( f(x) \). Determine \( \lim_{x \to 1} f(x) \).

CorrectIncorrect - Question 5 of 26
##### 5. Question

1 point(s)Category: K/U5. Consider the difference quotient: \( \frac{2(3+h)^4 – 162}{h} \). Which statements are true?

CorrectIncorrect - Question 6 of 26
##### 6. Question

1 point(s)Category: K/U6. The function \( y=f(x) \):

CorrectIncorrect - Question 7 of 26
##### 7. Question

1 point(s)Category: K/U7. The function \( y = f(x) \) has a removable discontinuity at:

CorrectIncorrect - Question 8 of 26
##### 8. Question

1 point(s)Category: K/U8. The value at \(\; f(7) \) is:

CorrectIncorrect - Question 9 of 26
##### 9. Question

1 point(s)Category: K/U9. The value of \( \lim_{x \to 1^+} f(x) \) is

CorrectIncorrect - Question 10 of 26
##### 10. Question

1 point(s)Category: K/U10. Which of the following is not a true statement about limits?

CorrectIncorrect - Question 11 of 26
##### 11. Question

1 point(s)Category: A11. A man drops a penny from the top of a 500 m tall building. After

*t*seconds, the penny has fallen a distance of s metres, where \( s(t)=500 – 5t^2, \; 0\leq t \leq 10 \). The velocity at \( t=5 \) isCorrectIncorrect - Question 12 of 26
##### 12. Question

1 point(s)Category: A12. Determine the slope of the tangent to \( f(x)=\frac{2}{\sqrt{x \, + \, 5} \) at the point where \( x=5 \).

CorrectIncorrect - Question 13 of 26
##### 13. Question

1 point(s)Category: A13. Evaluate the limit: $$ \lim_{x \to -5^+} \frac{5x}{x + 5} $$

CorrectIncorrect - Question 14 of 26
##### 14. Question

1 point(s)Category: A14. Evaluate the limit, if it exists: $$ \lim_{x \to 1} \frac{x^2 – 3x + 2}{x \, – 1} $$

CorrectIncorrect - Question 15 of 26
##### 15. Question

2 point(s)Category: A15. Evaluate the limit: $$ \lim_{x \to 125} \frac{125 – x}{x^{\frac{1}{3}} – 5} $$

CorrectIncorrect - Question 16 of 26
##### 16. Question

2 point(s)Category: A16. Consider the function \( f(x) = \begin{cases} \frac{x^2 – 9x + 20}{x – 5}, & \text{if} \; x \neq 5 \\ -1, & \text{if} \; x = 5 \end{cases} \).

Determine \( \lim_{x \to 5} f(x) \).

CorrectIncorrect - Question 17 of 26
##### 17. Question

1 point(s)Category: C17. The difference quotient finds the

CorrectIncorrect - Question 18 of 26
##### 18. Question

1 point(s)Category: C18. This function:

CorrectIncorrect - Question 19 of 26
##### 19. Question

1 point(s)Category: C19. This function:

CorrectIncorrect - Question 20 of 26
##### 20. Question

1 point(s)Category: C20. Complete the sentence by filling in the blank.

The derivative of a function represents the of a tangent at any point on the function.

CorrectIncorrect - Question 21 of 26
##### 21. Question

1 point(s)Category: A21. A soccer ball is kicked into the air from a platform. The height of the ball, in metres, \( t \)seconds after it is kicked is modeled by \( h(t) = -4.9t^2 + 13.5t + 1.2 \). Find the instantaneous rate of change 2 seconds.

CorrectIncorrect - Question 22 of 26
##### 22. Question

2 point(s)Category: T22. Determine the coordinates of the point on the curve \( y = \sqrt{x – 1} \) , where the tangent is perpendicular to the line \( 4x + y + 1 = 0 \).

CorrectIncorrect - Question 23 of 26
##### 23. Question

2 point(s)Category: T23. Given \( f(x)= \begin{cases} \; ax^2 + bx + c, & \text{if} \; x \lt 2 \\ (2 – x)^3 + 10x, & \text{if} \; x \ge 2 \end{cases} \)

\( f(x) \) is continuous at \( x = 2 \), has a y-intercept of 4, and at \( x = 1 \) the tangent to the curve is horizontal. Use these characteristics to find a, b, and c.

CorrectIncorrect - Question 24 of 26
##### 24. Question

2 point(s)Category: T24. $$ \textrm{Evaluate} \; \lim_{x \to -3^5} \frac{(x^{\frac{3}{5}} + 27)( x^{\frac{1}{5}} +3)^2}{x^{\frac{3}{5}} + 9x^{\frac{2}{5}} + 27x^{\frac{1}{5}} + 27 } $$

CorrectIncorrect - Question 25 of 26
##### 25. Question

1 point(s)Category: A25. A round balloon is being blown up so that its radius increases uniformly. Find the instantaneous rate of change of the surface area when the radius is 15 cm. Hint: What is the formula for the surface area of a sphere?

CorrectIncorrect - Question 26 of 26
##### 26. Question

2 point(s)Category: T26. Given that \( f(x) = \frac{\left|x + 1 \right|}{x + 1}, \; \; g(x) = \frac{x^2 – 1}{x – 1} \), evaluate $$ \lim_{x \to -1^-} \left[ f(x) – g(x) \right] $$

CorrectIncorrect