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algol [13]
3 years ago
5

Calculate dy/dx when y = (x2 + 2)e 4x as the derivative of a product, letting u = x2 + 2 and v = e4x . Which of the following is

a step in your solution?
A. dv/dx = 4xe3x
B. du/dx = 2x + 2
C. dv/dx = 4xe4x
D. du/dx = 2x
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

D. du/dx = 2x

Step-by-step explanation:

Given to find dy/dx where;

y=(x^{2} +2)e^4^x

Then when you let;

u=x²+2    and

v=e^{4x}

Then

In  u=x²+2  du/dx = 2x------------------------step 1

In e^4x, dv/dx = e^4x * d/dx (4x)

=e^4x *4 = 4e^4x------------------------------------step 2

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6 0
3 years ago
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7 0
3 years ago
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7 0
3 years ago
Question 1 (40 pt). You are given designs of 3 caches for a 16-bit address machine: D1: Direct-mapped cache. Each cache line is
BigorU [14]

Answer:

Step-by-step explanation:

a) What is the size of each cache?

Direct mapped cache= 2^index * size of cache line= 2^10 * 1B lines = 1KB.

2-way set associative cache= 2^index * size of cache line * 2 ways=2^7 * 4 words *2ways= 128 4B lines * 2 ways = 1KB

Fully associative cache= number of cache lines* size of each line= 256 * 4B lines = 1KB

b) How much space does each cache need to store tags?

Direct mapped cache= 1024 * 6-bit tags = 6Kb

2-way set associative cache= 256 * 7-bit tags = 1792 bits

Fully associative cache= 256 * 14-bit tags = 3584 bits

c) Which   cache   design   has   the   most   conflict   misses?   Which   has   the   least?    

Direct mapped cache has likely the most conflict misses, because it is direct mapped. Fully associative cache has the least since it is fully associative so it can never have conflict misses.

d) The   following   information   is   given   to   you: hit   rate   for   the   3   caches   is   50%,   70%   and   90%  but   did   not   tell   you   which   hit   rate   corresponds   to   which   cache,   which   cache   would   you   guess  corresponded   to   which   hit   rate?   Why?    

Since the size of all three caches is same size and as we said in the previous answer that direct mapped cache has more conflict misses and fully associative has the least so direct mapped will have 50%, 2-way set associative 70%, and Fully associative will have 90% hit rate.

e) Assuming   the   miss   time   for   each   is   20   cycles,   what   is   the   average   service   time   for   each? (Service   Time   =   (hit   rate)*(hit   time)   +   (miss   rate)*(miss   time)

We are given hit rates and miss rates. Also miss time=2o cycles for each cache and hit time= 1, 2, 5 for direct mapped, 2-way set associative and fully associative cache respectively.

Direct mapped= 0.5*1 + 0.5*20 = 10.5 cycles

2-way set associative= 0.7*2 + 0.3*20 = 7.4 cycles

Fully associative cache= 0.9*5 + 0.1*20 = 6.5 cycles.

6 0
3 years ago
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