Questions tagged 'Calculus'
92 questions
If z = f(x, y), where f is differentiable, and the following applies, find dz/dt when t = 1.?
Given that ( z = f(x, y) ), where ( f ) is a differentiable function, please find ( \frac{dz}{dt} ) when ( t = 1 ). The relationships are defined as follows: ( x = g(t) ) and ( y = h(t) ), with the sp...
How do I simplify 1-2sin^2x + sin^4x?
How can I simplify the expression (1 - 2\sin^2(x) + \sin^4(x))? I believe that using fundamental identities and factoring the expression will help, but I would appreciate detailed guidance on how to a...
need help on one calculus problem on continuous functions?
From the graph of the function ( g ), please identify the intervals where ( g ) is continuous. Select all that apply from the following options: ( (-\infty, -4] ) ( (-\infty, -4) ) ( [-4, -2] ) (...
Tan theta=4/3 ….piNovember 17, 2021 by thanh
I need assistance in finding the exact values for cos(θ/2) and sin(θ/2), given that tan(θ) = 4/3. Thank you!
Dec 20, 2024
How many molecules of sulfur trioxide are in 78.0 grams?
How can I calculate the number of molecules of sulfur trioxide (SO₃) contained in 78.0 grams?
I need help with these limit problems?
I need help with these limit problems: 1) If (2x - 1 \leq f(x) \leq x^2 - 2x + 3) for (x \geq 0), find (\lim_{{x \to 2}} f(x)). Evaluate the limit, if it exists. (If the limit does not exist, please e...
Particles traveling along space curves? collision?
Two particles are traveling along the space curves defined by ( r_1(t) = (t, t^2, t^3) ) and ( r_2(t) = (1 + 4t, 1 + 16t, 1 + 52t) ). Please find the points at which their paths intersect. If there i...
Dec 12, 2024
(1 pt) You are standing above the point (5,5) on the surface z=20-(x^2+y^2).?
You are standing above the point (5,5) on the surface defined by the equation z = 20 - (x² + y²). (a) In which direction should you walk to descend the fastest? Please provide your answer as a unit 2-...
Find the centroid for an area defined by the equations: y=2x+4 and y=((2x-3)^2)+1?
I am looking to find the centroid of an area defined by the equations ( y = 2x + 4 ) and ( y = (2x - 3)^2 + 1 ). I need to use integration for this calculation. Thank you for your help!
Dec 11, 2024
Please prove this: d/dx (csc x) = – csc x cot x ?
Could you please provide a step-by-step proof for the derivative of the cosecant function, specifically showing that ( \frac{d}{dx} (\csc x) = -\csc x \cot x )? I would appreciate any detailed explana...