Questions tagged 'Calculus'
92 questions
Jan 11, 2025
Using Dot Products of Vectors, Find a ⋅ b a = 8i + 6j, b = 4i + 5j?
How can I calculate the dot product of the vectors ( \mathbf{a} = 8\mathbf{i} + 6\mathbf{j} ) and ( \mathbf{b} = 4\mathbf{i} + 5\mathbf{j} )?
Jan 06, 2025
Calculus: Find an expression for the area under the graph as a limit?
Use the definition of a definite integral to find an expression for the area under the graph of the function ( f(x) = x^2 + \sqrt{1 + 2x} ) over the interval ( [5, 7] ). Please do not evaluate the lim...
find the differential of each function (CALCULUS HELP PLEASE)?
Could someone please help me find the derivatives of the following functions? ( y = \frac{s}{2 + 5s} ) ( y = u \cdot \cos(u) ) Thank you!
Jan 04, 2025
Evaluate the integral, where R is the triangle with vertices at….?
Evaluate the integral over the region ( R ), which is the triangle with vertices at (-8, 0), (0, 8), and (8, 0). The integral is given by: [ R \int (2x + y)^2 \, dA ] Please provide the exact answer i...
integrals of trigametrics?
What is the antiderivative of sin²(x)?
Jan 03, 2025
A car starts from rest and travels for 5.0 seconds with uniform acceleration of 1.5 m/s^2. The driver then…?
A car starts from rest and travels for 5.0 seconds with a uniform acceleration of 1.5 m/s². The driver then applies the brakes, resulting in a uniform acceleration of -2.0 m/s². If the brakes are appl...
Jan 03, 2025
Find 10 partial sums of the series. (Round your answers to five decimal places)?
I would like to find the first 10 partial sums of the series defined by the expression ( \sum_{n=1}^\infty \cos(8n) ). I have attempted to calculate these sums multiple times, but I struggle with the...
Parallel Axis Theorem?
Suppose a uniform slender rod has a length ( L ) and a mass ( m ). The moment of inertia of the rod about an axis that is perpendicular to the rod and passes through its center of mass is given by ( I...
How many photons are emitted per second? (1 watt = 1J/s )?
How many photons are emitted per second by a heat lamp that produces 24.0 watts of power at a wavelength of 6.8 micrometers? Given that 1 watt is equivalent to 1 joule per second, how can we calculate...
Consider the relation defined by the equation tan(y)= x + y for x in the open interval -2 pi < x < 2 pi?
Consider the relation defined by the equation ( \tan(y) = x + y ) for ( x ) in the open interval ( -2\pi < x < 2\pi ). a. Find ( \frac{dy}{dx} ) in terms of ( y ). b. Determine the coordinates o...