2 I 1 1 y=f(x) 2 lim {ƒ(x) – g(x)} x-1 A A/ 2 lim x⇒1 Use the functions f and g defined by the graphs in the above figure to determine the following limits. If the limit does not exist enter DNE. y g(x) f(x) g(x) 1 2 X & lim g(x) - S(x) A A MacBook Pro lim_ f(g(x)) x →0

Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. a=1/₁6 = ² C…

A:

Q: 5. Find a fundamental matrix of the following system and apply x(t) = $(t)Þ(0)¯'¹x to find a…

A:

Q: Find the point(s) at which the given function equals its average value on the given interval. f(x)…

A:

Q: fter t hours a freight train is s(t) = 17t² - 2t³ miles due north of its starting point (for 0 ≤ t ≤…

A:

Q: Find the first and second derivatives of the function. g(t) = (5t² - 9)² (9t²) g '(t) = 18t(51²-9)²…

A: Note:-Since you asked multiple questions ,according to our policy we can solve only first question…

Q: Find all values c which satisfy the conclusion of the Mean Value Theorem: f(x) = 4x² - 5x + 6, on…

A: The given polynomial function

Q: e. lim x* sin ¹ 137) 2x²+3x x-0

A: In this question, we want to find the limit of the given expression.

Q: Suppose ƒ(x) = (x − 1)(x − 5)³ + 10. Find the absolute extrema of f on each of the following…

A:

Q: Consider the function f(x) = x² - 7x + 10 x + 5 a. Find the first derivative. f'(x) b. List any…

A: Since, you have posted multiple questions, as per guidelines, we are supposed to answer only first…

Q: 7. Find the linearization L(x, y, z) of f(x, y, z) at the point Po. Find an upper bound for the…

A:

Q: Suppose f(x) = xe-7x Absolute minimum: ( Absolute maximum: ( 0≤x≤ 2. Use the Closed Interval Method…

A:

Q: Find the third derivative of the given function. 5 ₂() - (()*²-2) g =

A: Given:We are required to:

Q: Suppos the second derivative of f(x) "given by F"(x) = S(x² +49) 2 (36-x²213 Determine the intervals…

A:

Q: 8. Suppose $2000 is invested in an account that earns 6.25% interest compounded continuously. The…

A:

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y"+y' - 20y = 0, y(0)…

A: To solve the initial value problem by using the method of Laplace transforms., ,

Q: The following statement is true by mathematical induction: 1+2 +2² +2³+24+ + 2n-1=2"-1 for all…

A:

Q: Find parametric equations of the line that contains the point P(-2, 1, -3) and intersects the line…

A:

Q: What is the result of the following limit? O lim 3x x→∞ √9x² 1 3 1 3 23 2|3 +∞ 4x + 4

A:

Q: Determine the global extreme values of the function f (x, y) = x³ + x²y + 4y² on x, y ≥ 0, x + y ≤…

A:

Q: y = In[x. 4*]

A: We have to differentiate the given function.…

Q: Give a graph of the polynomial and label the coordinates of the intercepts, stationary points, and…

A:

Q: Use the Chain Rule to find dw/dt. dw dt www xey/z, x = t³, y = 2-t, w = xey/z √(³) (31. e 3t Need…

A:

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: Given

Q: Evaluate. (Be sure to check by differentiating!) [(8+xº) ³x7 dx

A:

Q: 2. By changing to polar coordinate, evaluate (b) x³y d4, where R is the upper half of the annulus…

A:

Q: Find the absolute maximum and minimum values of the function, and sketch the graph. 7x+1, for 1sxs1…

A:

Q: Find a) any critical values and b) any relative extrema. t(x) = x + +7x-1

A:

Q: Tell me about object sets.

A: We have to define Object sets.

Q: Find the location of the absolute extrema of ƒ(x) = = Absolute maximum at x= Absolute minimum at x =…

A:

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: Given that to find the interval of convergencelet  and using ratio test then limit

Q: 0 f. f(t) = t-1 3-t t 2

A:

Q: Find S₁1= 11 a-1 a for the following series: 1 - 5 +25 - 125 +...

A: We know that the geometry series common difference are same

Q: Suppose a spherical balloon is inflated at a rate of 100cm^(3) per minute. How fast is the radius of…

A: Formula of volume isWhere r is the radiusAnd the formula of derivative is

Q: Write the expression in terms of first powers of cosine. Do not use decimals in your answer. Make…

A:

Q: The price of parrafin wax to make candles is 56.5VND/cm³. Calculate the cost of wax to make a…

A:

Q: Tutorial Exercise Find the average value have of the function h on the given interval. h(u) = (14 -…

A:

Q: Find an e equation for the tangent line to the curve y = x √√3x² + 4 at the point (2,8)

A:

Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: The solution is shown in step-2

Q: A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base…

A:

Q: Use cylindrical coordinates to find the volume of the solid that is enclosed by the zone z =x^2 +…

A:

Q: The independent variable x is missing in the given differential equation. y²y" = y'

A:

Q: Evaluate the integral using integration by parts. [x8x dx

A:

Q: Find the area under the given curve over the indicated interval. y=x²; [0,5]

A:

Q: Determine the vertical asymptote(s) of the function. If none exists, state that fact. 9x - 2 X-8…

A:

Q: Sketch the graph of the following function. Indicate where the function is increasing or decreasing,…

A: To sketch the graph of the following function. To indicate where the function is increasing or…

Q: Find the derivative of: 5e-8 sin (-2x²)

A:

Q: (a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a. m= (b)…

A:

Q: If a rock is dropped from a height of 110 ft, its poistion t seconds after it is dropped until it…

A: The solution is shown in step-2

Q: Find the third derivative of the given function. g(t) = √11t + 10 g"(t) = 0 3993 8 (11t+10)

A: