Q1. The definition of the first derivative of a function f(x) is

Q2. The exact derivative of f(x)=x³ at x=5 most nearly is

25.00
75.00
106.25
125.00

Q3. Using the forward divided difference approximation with a step size of 0.2, the derivative of

f(x)=5e^2.3x at x=1.25 most nearly is
258.8
163.4
211.1

203.8

Q4. A student finds the numerical value of d/dx(e^x)=20.220 at x=3 using a step size of 0.2.  Which of the following methods did the student use to conduct the differentiation?

Backward divided difference

Calculus, that is, exact

Central divided difference
Forward divided difference

Q5. Using the backward divided difference approximation,  d/dx(e^x)=4.3715 at x=1.5 for a step size of 0.05.  If you keep halving the step size to find d/dx(e^x) at x=1.5 before two significant digits can be considered to be at least correct in your answer, the step size would be (you cannot use the exact value to determine the answer)

0.05/2
0.05/4
0.05/8
0.05/16

Q6. The heat transfer rate q over a surface is given by

where

       k = thermal conductivity (J/s-m-K) ,

       A= surface area (m²),

       T = temperature (K),

       y = distance normal to the surface,

the temperature T over the surface varies as

        T=-1493y³+2200y²-1076y+500,

        k=0.025 (J/s-m-K),

        A=3 m²

The heat transfer rate q in Watts at the surface most nearly is

-1076
37.5

80.7
500

Complete Solution

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