MCV4U1 - UNIT 1 - INTRODUCTION TO CALCULUS TEST ROUND ALL ANSWERS TO THE NEAREST TENTH, UNLESS OTHERWISE STATED. 1) Evaluate each of the following limits. All answers should be exact. (K - 1,2,2,3,2,2 marks) Vx + 20 +25 a) lim 3x +7x-20 b) lim x +5 -4 x- +3x -4 c) lim 2x - 20 d) lim Vx -5-5 x10 x-6-2 r-130 x -130\f2) Use the difference quotient method to determine the equation of the tangent to the graph of f(x} = x1 2x+ 13 where x = 3. (A 4 marks) 3) For the graph of y = f(x} shown below, determine each of the following limits. (A 4 marks} a) limfr): e) LiBfU) = d) i_133x)= 4) As a snowball melts, it's volume decreases. The volume in cubic centimetres is given by the 4 equation V(r) = - m', where r is the radius in centimetres. Determine, to the nearest tenth, 3 the rate of change of the snowball's volume when its radius is 10 cm. (A - 4 marks)5) For the following function, lim f(x) =8. Determine the values of a and b. (I - 6 marks) - 3ax' -4b, x5-2 f(x) = ax + b, x>-26) Determine the coordinates of the points on the graph of fig) = x3 + 31c2 21x+ 2 at which the tangent is parallel to the line Euc Zy =19. {I 6 marks) 7) While engaged in an intense conversation about limits, Karlo claimed that lim vx + 12 is x--12 equal to 0. Is Karlo's claim correct? Explain. (C-3 marks)8) A few days after their intense conversation about limits, Jenny and Karlo went on a date. While they were enjoying their meal, Jenny told Karlo that the expression f(x) - f(5) is the x - 5 slope of the tangent line to f(x) at the point where x = 5. Is Jenny's claim correct? Explain. (C-3 marks)