Numerade

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Question 1: 6 Marks Determine the following limits: (1.1) $$ \lim_{x \to -1} \frac{x^3 - 2}{x^4 + 4x - 3} $$ (1.2) $$ \lim_{x \to 3} \frac{x^3 - 8}{x^2 - 4} $$ Question 2: 22 Marks Differentiate the following to the appropriate independent variable and simplify where possible: (2.1) $$ y = \frac{1}{x} - \sqrt{\cos x} $$ (2.2) $$ y = (x^3 + 2)(x^2 - 2x + 1) $$ (2.3) $$ y = \frac{\sqrt{1 + \tan^2 x}}{\sec^2 x} $$ (2.4) $$ y = \ln e^x \left| \frac{x - 2}{x + 3} \right| $$ Question 3: 4 Marks The loading distribution y on a beam is given by $$ y = -25x^2 + 45x $$ Question 4: 9 Marks Given the curve $$ y = 2x^3 + 3x^2 - 12x $$. Find the turning points and the intercepts with the axes. Sketch the curve.

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2) Using the information from the previous problem, a) Determine the Electric field vector at point A which lies on the midpoint of the triangle's base. b) Determine the Electric Potential at A c) Determine how much work was needed to assemble that configuration of charges

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#15 Give an equation of a line that is parallel to $r(t) = \langle 3t-2, -t+4, 5t+1 \rangle$ and hits the xy plane when x = 2 and y = 4. Write your final answer as a vector equation. #16 Give an equation of a line that is perpendicular to the xz plane and passes through the point (3,7,9)

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Find a linearization that will replace the function over an interval that includes the given point $x_0$. Center the linearization not at $x_0$ but at a nearby integer, $x = a$, at which the given function and its derivative are easy to evaluate. $f(x) = \sqrt[4]{x}$, $x_0 = 16.4$ Set the center of the linearization as $x = $

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Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry.\\ $\int_{-1}^{1} \sqrt{1 - x^2} dx$

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Treatment of trichomoniasis includes: a. ceftriaxone 500mg IM x 1 dose b. metronidazole 0.75% gel PV q hs x 5 days c. azithromycin 1gm PO x 1 dose d. tinidazole 2gm x 1 dose 2. Treatment of bacterial vaginosis includes: a. ceftriaxone 500mg IM x 1 dose b. metronidazole 500mg BID PO x 7 days c. azithromycin 1 gm PO x 1 dose d. tinidazole 2gm PO x 1 dose 3. The new treatment guidelines for Gonorrhea include: a. Ceftriaxone 125mg IM plus Azithromycin 1 gm PO b. Ceftriaxone 250mg IM plus Azithromycin 1 gm PO c. Ceftriaxone 500mg IM d. Azithromycin 2gm PO 4. The most commonly reported STI in the United States is: a. Syphilis b. Gonorrhea c. Herpes d. Chlamydia 5. Treatment for Herpes Type 1 orally includes: a. Valacyclovir 2 gm PO x 1, repeated in 12 hours b. Acyclovir 400mg PO 3 times a day for 7-10 days c. Famciclovir 250mg three times a day for 7-10 days d. Valacyclovir 1gm PO x 1, repeated in 12 hours

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Which of the following is TRUE, regarding the Krebs Cycle During the Krebs Cycle, Acetyl-CoA is oxidized to form 3 molecules of NADH, 1 molecule of FADH2, 2 molecules of CO2, and 1 molecule of GTP During the Krebs Cycle, Acetyl-CoA is oxidized to form 6 molecules of NADH, 2 molecules of FADH2, 4 molecules of CO2, and 2 molecules of GTP During the Krebs Cycle, Glucose is oxidized to form 6 molecules of NADH, 2 molecules of FADH2, 4 molecules of CO2, and 2 molecules of GTP During the Krebs Cycle, Pyruvate is oxidized to form 3 molecules of NADH, 1 molecule of FADH2, 2 molecules of CO2, and 1 molecule of GTP Question 8 Which of the following is TRUE, regarding the Electron Transport Chain? During the steps of the Electron Transport Chain, electrons and H+ ions from NADH and FADIH2 are transferred to ADP and phosphate to form ATP by Substrate Phosphorylation During the steps of the Electron Transport Chain, electrons and H+ ions from NADH and FADH2 are transferred to ADP to form ATP by Oxidative Phosphorylation During the steps of the Electron Transport Chain, electrons and H+ ions from NADH and FADH2 are transferred to Oxygen, and ATP is generated by Oxidative Phosphorylation During the steps of the Electron Transport Chain, NADH and FADH2 are oxidized to form Oxygen and ATP, through Oxidative Phosphorylation

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Problem 5 (10 points) Design the inverter circuit in Fig. 5 to provide V_on = 1.2V, V_oi = 50 mV, and so that the current at the output is high when V_in is low. Fig. 5: The Simple Resistively Loaded MOS Inverter

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1. \ddot{x} + 7\dot{x} + 10x = 20 \qquad x(0) = 5, \dot{x}(0) = 3 2. \ddot{x} + 14\dot{x} + 85x = 170 \qquad x(0) = 0, \dot{x}(0) = 0 3. 4\ddot{x} + 7\dot{x} = 6te^{-5t} + e^{-3t} \qquad x(0) = 5

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Consider an n-channel Si-based MOSFET with an n?-polysilicon gate and an oxide thickness of 10 nm. The oxide has a fixed charge of 8 x 10?? C. This device is built on a substrate with a doping concentration of 10¹?/cm³. The work function difference between the gate and substrate is -1.5V. The channel length is 2µm and the channel width is 40µm. The effective carrier mobility is 150 cm²/V*s. Calculate: a. The minimum gate voltage required to induce a channel b. For a gate voltage of 2V and a drain voltage of 0.1V, calculate the drain current.

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gabrielle b.