The limit lim h 10 /36 + h – 6 h represents the derivative of some...
Compute the given derivative: 6. (5x-74 7. Find the limit: lim ho h+ 22 h - -8. Given: f(x) = x-3x+5: Find the maximum and minimum at the critical values
Find the value of the limit below. lim [6 – 5(x + Ax)]2 - (6 - 5x)2 Ax = 0 Δx Specify the function f for which this is the derivative. f(x) =
2. Use the limit theorems to find the following limit. r? +10x + 25 lim x+5 Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f(x+h)-f(x) f'(x) = {im What is the slope of tangent line to this curve at x =-1?
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
Find the following trigonometric limit: lim sin - Hint the substitution [((u-1)E)s01 u= t-n makes life 1. tm easier. Work inside the [...] first and then take the sine of your result, that is, use the rule that allows you to take the limit inside the sine function: lim sin(f(x)) n(Hm/s) sin x-a 2. Use the results we derived in class for power functions to find the derivative of g(x) (3x4 + v 4 atx Ans 3. When a function...
In the following, remember that f(n)(x) represents the nth derivative of f, and assume s > 0. (a) By giving an appropriately diverse selection of samples functions f, explain why it is reasonable to assume that for “most” functions f, there is some value s for which lim x→∞ f(x)e−sx = 0. (In other words, pretend you’re the teacher of a differential equations class trying to convince the class that this assumption is a reasonable one! Don’t just claim the...
Evaluate the limit, if it exists. (If it does not exist, enter NONE). . (6+h)– 36 lim h0
Thank you. - Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = g(x) lim f(x)= lim g(x) = f(x) x- lim x+0 g(x) lim lim g(x) = lim [f(x)+g(x)] = x-1 lim f(x) = lim g(x) = lim --+ f(x) h- h derivative of f(x) = 2x² + 3x is f'(x) = 4x +3. The steps are what count here!...