To calculate the slope of a curve, you need to calculate the derivative of the curve's function. The derivative is the equation of the slope of the line tangent to the point on the curve whose slope you want to calculate. It is the limit of the curve's equation as it approaches the ...
Use the equation given to calculate the slope of a line tangent to {eq}y=4x^2+3x{/eq} at {eq}P(-3,27){/eq}. {eq}m_{PQ}=\frac{f(x_1+h)-f(x_1)}{h}{/eq} Slopes and Tangents: To find the slope o the curve, we can...
You might also be interested in ourcosineandtangentcalculators. Law of Sines TheLaw of Sinesdescribes the relationship between the sides and angles of oblique (scalene) triangles. sin(α)/a=sin(β)/b=sin(γ)/c You can use the Law of Sines to solve for the angle or side of any triangl...
If you graph the arctan function for every possible value of tangent, it forms an increasing curve over all real numbers from (-∞, –π/2) to (∞,π/2). Horizontal asymptotes occur at y = –π/2 and y = π/2, which coincide with the values of the vertical asymptotes of the ta...
Apply the chain rule in the problem below;df(u)dx=dfdu⋅dudx As per the requirement, we have also use the product rule and the product rule. The quotient rule is given by: (fg)′=f′⋅g−g′⋅fg2 The product rule is given as; ...
The curvature of a curve at any point is defined as the rate of arc of rotation of the tangent of that curve. The radius of curvature of the curve is the reciprocal of the curvature. The curvature is found by the formula {eq}\kappa = \dfrac{{\left| {\vec r'\left( t \right)...
When an object moves along a circular path, a distance r from the center of this circle, then the object's speed is tangential to the circle at any point. What does the term "tangential" mean in this context?: A tangent in mathematics is a line that touches a curve at a single ...
Integral calculator helps you solve definite and indefinite integrals (antiderivatives) of a function step by step for free. Try it now!
To convert the superelevation ratio into an angle, take the inverse tangent of the ratio. The resultant is the angle of the roadway bank in degrees. Using the previous calculation, tan(Θ) = 0.4, so Θ = tan^-1(0.4) = 21.8°. This is the minimum bank angle to avoid relying on fric...
I must look for the interval where the point travels more distance in the less time. When I'm asked to find the point where the instantaneous speed is equal to the average speed, I must find the point where its tangent line (slope/derivative) is equal to the line from the origin to ...