25,270 Answered Questions for the topic calculus

Calculus

12/01/23

if A={*,/,+,-,}, find A
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Calculus

12/01/23

if A={*,/,+,-,}, find A
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Calculus Math

12/01/23

Implicit Derivative (no calculator)
4x2 + 2xy + y2 = 12Could someone explain what the steps/rules used for each step are rather than provide the answer? Thank you!
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Calculus

12/01/23

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=6-x2, y=2; about the x-axis x=2-y2, x=y4; about the y-axis y=x3, y=1, x=2; about y=-3 y=x2, x=y2; about x=-1 I can sketch the graph but I'm not sure how to proceed with the calculation of the... more
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Calculus

12/01/23

If f is continuous, prove the equation below and evaluate.
Part 1: if f is continuous, prove that(0,π/2) ∫f(cosx)dx=(0,π/2) ∫f(sinx)dxPart 2: Use the exercise above to evaluate (0,π/2) ∫cos2(x)dx=(0,π/2) ∫sin2(x)dx
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Calculus

12/01/23

Evaluate the integral using substitution
∫x2√(2+x)dx 0, 1 ∫(3t-1)50dt -π/3, π/3 ∫x4sinxdx
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Calculus

12/01/23

Find the area between the curves for the given interval. What does the area represent?
If the birth rate of a population is b(t)=2200+52.3t+0.74t2 people per year and the death rate is d(t)=1460+28.8t people per year, find the area between these curves for 0≤t≤10. What does this area... more
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Calculus

12/01/23

Finding local extrema
Consider the family of functions f(x)= a cos +(sinx)^2, where the parameter a varies over the interval (0,3). The locations of the local extrema of functions in this family depend on the parameter... more
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Calculus

12/01/23

maximum and minimum
Find the maximum and minimum values attained by the given function on the indicated closed interval.f(x) = 3x^2 - 5x^3 [-2,2]
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Calculus

12/01/23

If the derivative of a continuous function f is undefined at x = c, f can be increasing at x = c.
title
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Calculus

12/01/23

AP Calculus BC - Integration
Find the derivatives of each function: h(x) = 2∫1/x arctan(t) dt H(x) = 2∫x^2 (w-1)/(√w) dw g(x) = tan x ∫x^3 √t sin (t) dt
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Calculus

12/01/23

Maximum and Minimum
Find the maximum and minimum values attained by the given function on the indicated closed interval.f(x) = 3x^2 - 5x^3 [-2,2]
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Calculus

11/30/23

Find displacement and distance traveled

The velocity function is v(t) = t^2-5t+6 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,6]displacement= distance... more
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Calculus Precalculus

11/30/23

pre calc 3.5 question
A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by y=Cx - (1 + C²) (g/2) (x/v)². in this formula, x is the horizontal distance in meters, y is the... more
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Calculus Math Trigonometry

11/30/23

Piecewise function question
Let 𝑔(𝑥) be the piecewise function defined as: [ 2/x+1 if x< -2 ] [ -4/x if -2≤x<0 ]g(x)= [ 0 if x=0 ] ... more
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Calculus

11/30/23

Maximizing profit

The weekly demand for a certain type of dog treat approximately satisfies the equation p=16-2x and the total cost of producing x units of dog treats is C(x)=50+4x. The quantity x is measured in... more
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Calculus

11/30/23

Calc 1 question
what are the concaves up and down and the inflection points step by step for ln(2+sin(x))
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Calculus Math

11/30/23

No calculator implicit differentiation: trigonometry
Could you explain how to solve this to someone who has never learned this before? I'm having trouble explaining this to my younger sister.Find dy/dx at the point (pi, pi/4) when sin x + sin y = tan... more
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Calculus Math

11/30/23

Vertical tangent lines
No calculator is allowed for this question.Find all points where vertical tangent lines exist for the graph of x2+3y2+6y = 6.A. (-1,3)B. (-1,3) and (-1,-3)C. (3,-1)D. (-3,-1) and (3,-1)
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Calculus Math

11/30/23

Implicit derivative at a point (no calculator)
Given the equation of the curve 2x2-3xy+y = 10, find dy/dx at the point (0, 10).A. -30B. 0C. 30D. 40
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Calculus Math

11/30/23

Find the slope, implicit differentiation (no calculator)
The slope of the tangent line to the graph of ln(x2y) = 2-x2 at the point where x = 1 is:A. -4eB. -3eC. 0D. 2e
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Calculus

11/30/23

Minimizing average cost

A wood pellet factory can produce x hundred units of wood pellets per day at a daily cost of C(x)=0.6x^2+21x+1215, in dollars.a. find the marginal cost b. Show that, when the average cost is at a... more
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Calculus

11/30/23

At a certain moment a 100-gallon mixing tank is full of brine containing 0.25 pounds of salt per gallon.

At a certain moment a 100-gallon mixing tank is full of brine containing 0.25 pounds of salt per gallon. Find the amount of salt present t minutes later if the brine is being continuously drawn off... more
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Calculus

11/30/23

A 200-liter tank, initially full of water, develops a leak at the bottom.

A 200-liter tank, initially full of water, develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank t minutes after the... more
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Calculus

11/29/23

Elasticity of Demand
Suppose a manufacturer can sell f(p)= -65p+5200 units of a product when the price is p dollars per unit.a. Determine the elasticity of demand, E(p), when the price is p=20 dollars.b. Is demand... more
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