Limits of Functions:The concept of limits are applied in the place where the derivative of the function is to be found. Here the rules of differentiation will be as per the formula: {eq}\displaystyle \lim _{h\to 0}\left[\frac{f\left(x+h\right)-f\left(x\right)}{...
Finding the derivative of a function is called differentiation. Basically, you calculate the slope of the line that goes throughfat the pointsxandx+h. Because we take the limit forhto 0, these points will lie infinitesimally close together; therefore, it is the slope of the function in the...
Explain each step with the rules used. How to take the derivative of x? How do I take the derivative of V(t) = 100(t + 3)e^{-0.02t}? How to take the derivative of e. Describe how you would approach taking the derivative of y = (x 2)^3 e^{4x} / x^7 (x...
)/hNow do a binomial expansion of (x+h)n (look up the Binomial Theorem). See the link below for the full derivation. It's a bit much to write out with this text editor.https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/power_rule...
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HallsofIvy Science Advisor Homework Helper 42,895 981 If you are required to use the definition of "convex" then use the fact that eta+(1−t)b=etaebe−bt Or are you allowed to use the fact that a function is convex if and only if its second derivative is positive for all ...
The Lagrangian is then: is an optimization prob- 1 3 ∑n L(π′) = O(π′, π) + λ 1 − πj′ j=1 The derivative of the Langrangian with respect to each πi′ is: ∂L ∂πi′ = −α − α log(πi′/πi) + vi − λ Setting each ...
General Steps to find the vertical tangent in calculus and the gradient of a curve: Find thederivativeof the function. The derivative (dy/dx) will give you the gradient (slope) of the curve. Find a value of x that makes dy/dx infinite; you’re looking for aninfinite slope, so the ve...
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Step 1:Find the velocity function.The velocity function is the derivative of the position function. So, to find the velocity function you need todifferentiates(t) = 4t2– 2t, using thepower ruleandderivative of a constant rule: v(t) = 16t – 4 ...