Root finding (root, brentq) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the root function from scipy.optimize.

SciPy

from scipy.optimize import [1]

result = root(lambda x: x**2 - 4, 1.0)
print(result.x)

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Acurve_fit

Bbrentq

Cminimize

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Importing 'brentq' instead of 'root'.

Using 'minimize' which is for optimization, not root finding.

The root function is imported from scipy.optimize to find roots of equations.

2fill in blank

medium

Complete the code to find the root of the function f(x) = x^3 - 1 using root with initial guess 0.5.

SciPy

from scipy.optimize import root

def f(x):
    return x**3 - 1

sol = root(f, [1])
print(sol.x)

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A0.5

B2.0

C-1.0

D1.0

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1.0 as initial guess instead of 0.5.

Using negative initial guess which is not required here.

The initial guess for the root is 0.5 as given in the instruction.

3fill in blank

hard

Fix the error in the code to correctly find the root of f(x) = cos(x) - x using brentq between 0 and 1.

SciPy

from scipy.optimize import brentq
import numpy as np

def f(x):
    return np.cos(x) - x

root_value = brentq(f, [1], 1)
print(root_value)

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A0

B1

C-1

D0.5

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 as the start of the interval which is the end.

Using negative values outside the valid interval.

The brentq method requires an interval where the function changes sign. The interval [0,1] is correct, so the first argument must be 0.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

SciPy

words = ['data', 'science', 'ai', 'ml']
lengths = {word: [1] for word in words if [2]

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Alen(word)

Blen(word) > 3

Cword

Dword > 3

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'word' instead of 'len(word)' for the value.

Using 'word > 3' which compares string to number.

The dictionary comprehension maps each word to its length using len(word). The condition filters words with length greater than 3 using len(word) > 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths only if length is greater than 2.

SciPy

words = ['cat', 'dog', 'a', 'elephant']
result = {{ [1]: [2] for w in words if [3] }}

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Aw.upper()

Blen(w)

Clen(w) > 2

Dw

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'w' instead of 'w.upper()' for keys.

Not filtering words by length.

The dictionary comprehension uses w.upper() as keys, len(w) as values, and filters words with length greater than 2 using len(w) > 2.