B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1) 3. limx-4(X2 + 3X – 5) (t+1)? 2(t2+3) 3w2-4w+2 4. limt-1 5. limw-2 w3-5
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A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…
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A: As per guidelines, we are supposed to solve only first 2 questions. Please repost other questions…
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A: We can solve this using the L'Hospital rule. And also from expanding equation we can solve easily.
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Q: 1. Use the graph to find the limits In (t + 2) f(t) = 2- -2 2 a) t→0 lim f(t) b) lim f(t) t→-1
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A: Please refer the attached image for complete solution.
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- Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.Calculate the difference d between the global maximum and global minimum values of f(x)=x2−4x+6 in the interval [−2,4].Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No 2. Yes
- evaluate the limit: limit of the square root of 1+t - square root of 1-t / t as t approaches 01. For what value (s) of x is the function f(x) = 4/2x2 - 6x not continous? 2. If the demand of firm is QD (p) = 50 -3p and its supply function is Qs (p) = 14 + 6p. What is the equilibrium? 3. Find Lim x2 -4x + 3/5How to find the the relative maximum or minmum of the function: e^(3x^2+4) with x and y coordinates
- Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular region whose vertices are (0,0), (6,0), and (0,4).For every solution y(x) of the equation y''+ 2y'+ 5y = 0 it is true that limx→∞ y(x) = 0. ?Let f(x)= -6x^4+8x^3+72x^2 a) f has a relative minimum at x= b) f has an inflection point at x= c) lim x-> +inf f(x) d) lim x-> -inf f(x)
- Find the absolute maximum and absolute minimum of the function f(x,y) = 20 - 2x + 5y on the closed triangular region with vertices (0,0) , (5,0) and (5,8).15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or NoFind the minimal distance between the point (3, 9) and the curve of the function f(x) = 9 − x^2