Problem

Find $ f $. $ f"(t) = t^2 + 1/t^2 $, $ \quad t…

01:20

Problem 41 Hard Difficulty

Find $ f $.

$ f"(0) = \sin \theta + \cos \theta $, $ \quad f(0) = 3 $, $ \quad f'(0) = 4 $

Answer

$$
f(\theta)=-\sin \theta-\cos \theta+5 \theta+4
$$

Discussion

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Video Transcript

take the integral of both sides the integral of sine as negative co sign data and a girl of coastline is signed data. And remember, we must out r c. Okay, now substitute end if of prime zeros four, then four is negative. One pus era policy there for five is our seed. Therefore we have now take the derivative and we get off of zero is basically the same thing again. We're taking fire. We're taking the integral again. Given the derivative we're taking the integral we can do. Note this with Kay cause our previous constant with C we're taking the interval twice. We get k equals for Therefore we get off with data. It's a negative sign of that, uh, minus coastline did, uh, because five data plus four.

Amrita B.

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem

Find $ f $. $ f"(t) = t^2 + 1/t^2 $, $ \quad t…

Problem 41 Hard Difficulty

Find $ f $.

$ f"(0) = \sin \theta + \cos \theta $, $ \quad f(0) = 3 $, $ \quad f'(0) = 4 $

Answer

$$
f(\theta)=-\sin \theta-\cos \theta+5 \theta+4
$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Find $ f $. $ f"(t) = t^2 + 1/t^2 $, $ \quad t…

Problem 41 Hard Difficulty

Find $ f $. $ f"(0) = \sin \theta + \cos \theta $, $ \quad f(0) = 3 $, $ \quad f'(0) = 4 $

Answer

$$f(\theta)=-\sin \theta-\cos \theta+5 \theta+4$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Heather Z.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Find $ f $.

$ f"(0) = \sin \theta + \cos \theta $, $ \quad f(0) = 3 $, $ \quad f'(0) = 4 $

$$
f(\theta)=-\sin \theta-\cos \theta+5 \theta+4
$$