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float 표현 방식 예제
(a)
1
print(1e3)
1000.0
(b)
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if 1e3 == 1000:
print(True)
else:
print(False)
True
(c)
1
print(1e-03)
0.001
(d)
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4
if 1E-3 == 1/1000:
print(True)
else:
print(False)
True
(e)
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2
str = "{:6.4f}".format(-1.408)
print(str)
1.4080
(f)
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2
str = "{:6.2f}".format(-1.408)
print(str)
-1.41
2
math package의 exp()함수
(a)
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import math
print (math.exp(0))
1.0
(b)
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import math
print(math.exp(1))
2.718281828459045
(c)
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2
import math
print(math.exp(1)*math.exp(1))
7.3890560989306495
(d)
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2
import math
print(math.exp(2))
7.38905609893065
(e)
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2
import math
print(math.exp(2)-math.exp(1)*math.exp(1))
8.881784197001252e-16
3
f() 함수에 대한 질문들
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2
def f(x):
return 1/math.exp(x**2)*math.cos(5*x) - 0.1
(a)
1
print(f(0))
0.9
(b)
1
print("{:5.4f}".format(f(-1.408)))
0.0001
(c)
1
print("{:5.4f}".format(f(-1.408176)))
0.0000
(d)
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2
print("{:5.4f}".format(f(-1.6)))
print("{:5.4f}".format(f(-1.4)))
-0.1112 0.0062
(e)
-1.46 < x < -1.39일때 f(x) == 0 되는 x가 존재하는가?
f(-1.46)는 음수고 (-1.39)sms didtndlek. Ekfktj f(x)는 0이 되는 지점이 이 구간 어딘가에 존재한다. 그래프를 그려보면 확실히 알 수 있음
4
함수를 인자로 받는 함수 crossing_finder()에 대한 질문들
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def crossing_finder(f,start=-10,end=10,n=100):
r = end - start
x_list = [i / n * r + start for i in range(n)]
y_list = [f(x) for x in x_list]
prev_x = x_list[0]
prev_y = y_list[0]
crossing_list = []
for i in range(1,n):
x = x_list[i]
y = y_list[i]
if prev_y * y < 0:
crossing_list.append((prev_x,x))
prev_x = x
prev_y = y
return crossing_list
(a)
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f = lambda x: 1/math.exp(x**2) * math.cos(5*x) - 0.1
c = crossing_finder(f)
for (start,end) in c:
print("({:6.4f},{:6.4f})".format(start,end))
(-1.6000,-1.4000) (-1.0000,-0.8000) (-0.4000,-0.2000) (0.2000,0.4000) (0.8000,1.0000) (1.4000,1.6000)
(b)
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def zero_finder(f,start,end,eps=1E-9):
x = (start + end)/2
y1 = f(start)
y = f(x)
y2 = f(end)
if math.fabs(y) < eps:
return x
elif y1*y < 0:
return zero_finder(f,start,x,eps)
else:
return zero_finder(f,x,end,eps)
ans_list = []
for (start,end) in c:
ans_list.append(zero_finder(f,start,end))
for i in range(len(ans_list)):
ans = ans_list[i]
print("ans[{1}] = {0:6.4f}".format(ans,i))
ans[0] = -1.4082 ans[1] = -0.9972 ans[2] = -0.2923 ans[3] = 0.2923 ans[4] = 0.9972 ans[5] = 1.4082
