Calculus II Introductory Quiz

Math 126 Introductory Quiz Fall 2018 Write neat, concise, and accurate solutions to each of the problems. No electronic devices are allowed. Evaluate 64.4 x 2.25. short way (4\cdot2^{\frac{1}{2}}\psi) long way 64.4 128. ५५.१ 1288 116.1 \[\frac{12.2.8}{144.90~0}\] Express 400/17 as a decimal, correct to the nearest hundredth. 23.5주 17400.000 17 Express [3\cdot\frac{20\cdot21\cdot41}{6}+4\cdot\frac{20\cdot21}{2}-4\cdot20] = (10(2(-4)+4\cdot21-8)) 10 (al-5-8) (a(9+5-8)) १३५० as an integer. Find the sum+ [\frac{7}{6}+\frac{4}{5}=\frac{39+24}{30}=\frac{59}{30}] [1+\frac{1}{2}+1-\frac{5}{7}=2-\frac{1}{30}=\frac{51}{20}] 120 is 80% of what mumber? 0.8 \(x=1220\) \[x=i20\cdot\frac{5}{4}=150\] \[120\rightarrow807a-Y\] 150 List the numbers 274, 0.4389 x 274, and 2740.8722 in increasing order. 0.4389-2742749 0.8722 (multifly by multiply by 7. Find the perimeter and area of a rectangle that has a length of 18 feet and a width of 7.5 feet. P = 2(18 + 7.5) = 36 + 15 = 52' + 15 = 140 square feet R 187.5=·= 28.5 = 140 square feet 8. Let f(x) = 1/2x^3 - 5/2x^2 + 4x. Compute f(4) - f(1). y(4) - y2(1) = φ42 - 40 + 16 - (12 - 12 + 4) al - a4 - 9. Express 4/(x+1) + 3/(2x-5) as a single fraction. 4/(x+1) + 3/(2x-5) = (8x-20+3x+3)/((x+1)(2x-5)) = (11x-17)/((x+i)(2x-5)) 10. Give the values of sin(π/3), cos(π/2), and tan(π/4). cos π/2 = 0 tan = 1 11. Use the technique of completing the square to find the vertex of the parabola y = x^2 - 6x + 20. y = x^2 - 4x + 20 = (x-3)^2 + 11 The vertex (3, 11) 12. Find all values of x that satisfy the equation x^2 = 13x. x^2 - 13xk = 0 κ(x-13) = 0 x = -√15, 0, √13 13. Find all values of x that satisfy the equation x²-4x=11. x²-4x-11=0 x=(4±√(16+44))/2 =2±√15 14. Find all values of x that satisfy the equation √(x²-9)=4. √(x²-9)=4 x²-9=16 x²=25 x=±5 15. Find the quotient when x³-2x²+7x-6 is divided by x-2 x-2√x³-2x²+7x-6 The quotient is x²-2x+3 Synthetic Division Method 1-2 7 -6 2 0 4 6 1 2 3 0 16. Evaluate lim(x→∞)(x³-4x+7)/(8+5x²+3x³). =lim(x→∞)(1-4/x²+7/x³)/(8/x³+5/x+3) = -1/3 17. Find f'(x) if f(x)=x³-4x²+3x+e^(4x+1)+2x¹ f'(x)=3x²-8x+3+e^(4x+1)(4)+2x¹ 18. Find g'(x) if g(x)=ln(x²+3x+5). g'(x)=(2x+3)/(x²+3x+5) 19. Find F'(2) for the function F(x)=x/(x²-1) F'(x)=(x²-1-x*2x)/(x²-1)² = -(x²+1)/(x²-1)² F'(2)=-5/9 20. Answer true or false for each of the statements a. (a+b)² = a² + b² (False) b. x⁻² = √x (False) c. √(-y)² = y (False) d. √(x²+y²) = x+y (False) e. (a²+b)/(ac) = (a+b)/c (False) f. (x-y)/z = x/z - y/z (True) 21. Sketch a graph of the function given on the figure.