Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The derivative of the function f is defined by f^(')(x)=(x^(2)+3)sin(2x). If f(4)=7, then use a calculator to find the value of f(-1) to the nearest thousandth. Answer:

The derivative of the function f f is defined by f′(x)=(x2+3)sin⁡(2x) f^{\prime}(x)=\left(x^{2}+3\right) \sin (2 x) . If f(4)=7 f(4)=7 , then use a calculator to find the value of f(−1) f(-1) to the nearest thousandth.\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Evaluate variable expressions for sequencesright chevron icon

Full solution

Q. The derivative of the function f f is defined by f′(x)=(x2+3)sin⁡(2x) f^{\prime}(x)=\left(x^{2}+3\right) \sin (2 x) . If f(4)=7 f(4)=7 , then use a calculator to find the value of f(−1) f(-1) to the nearest thousandth.\newlineAnswer:
  1. Integrate f′(x)f'(x): To find the value of f(−1)f(-1), we need to integrate the derivative f′(x)f'(x) to get the original function f(x)f(x). We will then use the initial condition f(4)=7f(4) = 7 to find the constant of integration.
  2. Use initial condition: First, we integrate f′(x)=(x2+3)sin⁡(2x)f'(x) = (x^2 + 3)\sin(2x). This requires integration by parts or a special technique since it is a product of a polynomial and a trigonometric function. However, we cannot directly integrate this without more information or a different approach because the problem asks for the value of f(−1)f(-1) and not the general form of f(x)f(x).

More problems from Evaluate variable expressions for sequences

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 3 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 2 months ago

View all (20)