Question

Notify Me Bookmark

(a) Estimate the area under the graph of f(x) = 10/x from x = 1 to x = 5 using four approximating rectangles and right endpoints. R4 = (b) Repeat part (a) using left endpoints. L4 = (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. 1. L4 2. R4

(a) Estimate the area under the graph of f(x) = 10/x from x = 1 to x = 5 using four approximating rectangles and right endpoints. R4 = (b) Repeat part (a) using left endpoints. L4 = (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. 1. L4 2. R4

Image text
(a) Estimate the area under the graph of f ( x ) = 10 / x from x = 1 to x = 5 using four approximating rectangles and right endpoints.
R 4 =
◻ (b) Repeat part (a) using left endpoints.
L 4 =
◻ (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underestimates, or is the exact area. ? ◻ 1. L 4 ? ? ◻ 2. R 4

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

Two CMOS inverters are connected together as shown below (Fig. 2.1). If it is needed in calculations, please use the following assumed data: gate oxide thickness tox = 7.6 nm for silicon dioxide (SiO2); built-in voltage V bi = 0.7 V; zero-bias bottom-area junction capacitance (normalised) Cj0An = 1.10 × 10−4 F/m2 ; zero-bias sidewall capacitance (normalised) Cj0swn = 2.19×10−11 F/m; state your assumption clearly if other additional data are needed. Sizes of M1 to M4 : Fig. 2.1 (W/L)n = 0.4µm/0.2µm (W/L)p = 1.0µm/0.2µm (a). With the input waveform shown in Fig. 2.1, at time t1, what are the expected operation modes respond to the given input waveform. (b). Determine the dominant drain capacitance of M2 at time t1. Assume the worst case of the sidewall capacitance contributed from four sides. (c). Determine the dominant gate capacitance of M3 at time tl. (Hint: the bulk terminal of each of the MOSFET is connected to either ground or VDD). (d). Draw a sketch comparing the output waveform with the input signal, taking into account the qualitative effects of capacitance within the MOS transistors.
Solution
0 0

Two CMOS inverters are connected together as shown below (Fig. 2.1). If it is needed in calculations, please use the following assumed data: gate oxide thickness tox = 7.6 nm for silicon dioxide (SiO2); built-in voltage Vbi = 0.7 V; zero-bias bottom-area junction capacitance (normalised) Cj0An = 1.10×10-4 F/m2; zero-bias sidewall capacitance ( normalised) Cj0swn = 2.19×10-11 F/m; state your assumption clearly if other additional data are needed. Sizes of M1 to M4 : (W/L)n = 0.4μm/0.2μm (W/L)p = 1.0μm/0.2μm (a). With the input waveform shown in Fig. 2.1, at time t1, what are the expected operation modes of the two n-type MOSFETs respectively? Assume that the inverters are fast enough to respond to the given input waveform. (5 marks) (b). Determine the dominant drain capacitance of M2 at time t1. Assume the worst case of the sidewall capacitance contributed from four sides. (10 marks) (c). Determine the dominant gate capacitance of M3 at time t1. (Hint: the bulk terminal of each of the MPSFET is connected to either ground or VDD ). ( 6 marks) (d). Draw a sketch comparing the output waveform with the input signal, taking into account the qualitative effects of capacitance within the MOS transistors. (4 marks)
Solution
0 0

Let f(x) = 4x − x2, 1 ≤ x ≤ 2, and let S be the region that lies under the graph of f and above the x-axis. Estimate the area of the region S using five approximating rectangles, and right endpoints. What is the estimated area? Do not round the answer. Type the value of the estimated area. Answer: Check

Solution
0 0