Define f(5) in a way that extends f(s) = f(5)= s³ - 125 3 S s²-25 to be continuous at s = 5. (Type an integer or a simplified fraction.)

Q: For what value of a is the following function continuous at every x? a ²x-2a, x≥2 24, x<2 f(x) =…

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Q: 2 If √7-4x² ≤ f(x) ≤ √√7-x² for -1 ≤x≤ 1, find lim f(x). x→0 lim f(x) = x→0 (Type an exact answer,…

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Q: Question Use a power series to represent the function f(x) Sorry, that's incorrect. Try again? £ £ 1…

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Q: 1. Given the function f(x) = 4x3 + 12x² 15x + 2, a) Find the first derivative and the critical…

A: Given function:- f(x) =4x3 +12x2 -15x + 2

Q: #37) (modified) Find the equation if the tangent line at the point x=1: y = x4 + 1/x - 3ex

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Q: In the following exercises, express each series as a rational function. 69. n=1 x"

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Factoring this, we get F(x)=2x3+24x+12x3² + 12x + 6). Since is never 0, then F(x)=0 when x² 12x+6=0,…

A: Given:- f''x=2x-3+24x-4+12x-5

Q: 4. A ceramic insulator is baked at 400C° and cooled in a room in which the temperature is 25C°.…

A: Concept: The formula used is the rate of cooling dθdt=k(θ-θ0) Here θ is the temperature of the body…

Q: Evaluate lim x 1 expression. x² In²x - 2x + 1 Identify the indeterminate form of the given

A: Given query is to find the limit of the expression.

Q: 2. A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a…

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Q: 7 Graph R(x)= x² -+4x-5 x²+x-2 (lis steps, :) list all steps

A: Find the vertical asymptotes by setting the denominator equal to zero and solving for x. Since it is…

Q: QUESTION A10 (5 The equation of a straight line given y = bx + a, where b is equal to +5. What can…

A: y=bx+a where b = 5   y = 5x + a   here b = 5  is slope of the line.

Q: 24 Which of the following functions is not differentiable on all of its domain? Select one…

A: We have given functions (i) fx=x+1ex Differentiable everywhere on its domain.  (ii) fx=x2-1 This is…

Q: Which of the following integrals is the area between the graph of f(x) and the y-axis from b to c…

A: Given graph:-

Q: 6х3 + 2х2 +22х 2х2 +5

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Q: 7.5. Find a, b, c so that the function w = (ay³ + ix³) + xy(bx + icy) is analytic. If z = x+iy,…

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Q: H..W... solve the following equat.1.9.1.2...... •2x+y=1" H.......

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Q: Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x³ - 12x + 9

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Q: The integral in this exercise converges. Evaluate the integral without using a table. 1² -2 - 00 Oe…

A: Given query is to find the value of the integral.

Q: Let f(x) = (4sin x + 8 cos x)arctan a ƒ'(x) =

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Q: Find and classify the stationary points of (a) y = x  e- x (b) y = ln(x) - x

A: For stationary point of the function , the derivative is equal to zero .

Q: Find the derivative of the function. f(x) = 6(x³ + x)³

A: I am attaching image so that you understand each and every step.

Q: 2 #fL = √ x² + y²₁ dL dt dx dt = 1, dy dt = -3, find (Simplify your answer.) dL dt when x = 12 and y…

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Q: Escoge la mejor contestación 1. Identifique la superficie cuadrica 2² =²+² 16 a. Cono elíptico b.…

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Q: B E A B Q: ABCD is quadrilateral Shape whose diameters. intersect at E, Sinc AB / CD // EF, and F in…

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Q: Use f(2)=9z+12 and g(z) = 2z - 15 to find (fog)-¹(z) 1. (Jag) ¹(2)=(-123) 18 2. (fog)(2)- 3.…

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Q: Find T-4 2-4

A: We have to find  limx→4- x-4x-4.

Q: Work the following application problems 7.) The daily cost of producing x high-performance wheels…

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Q: A tank contains 80 gal of pure water. Brine solution with 2 lb/gal of salt enters at 2 gal/min, and…

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Q: Show using the MVT the equation x^3-x-2 = 0 has one real solution on the interval [1,2] AND…

A: Using mean value theorem f'c=fb-fab-a Where, a=1,b=2 f'x=3x2-1 f'c=3c2-1 f2=23-2-1=5 f1=13-1-2=-2

Q: QUESTION 10 Let W (s, t) = F(u(s, t), v(s, t)) where u(1,0)=-4,u,(1,0) = -7, u₂(1,0) = -4 v(1,0) =…

A: Here  ⇒wss,t=∂w∂u×∂u∂s+∂w∂v×∂v∂s ⇒wts,t=∂w∂u×∂u∂t+∂w∂v×∂v∂t

Q: Consider the following integral. [√1+7x dx Find a substitution to rewrite the integrand as 1/3 7 U =…

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: Given function of profit as, P=140x-x2800-1900 where x=units of products produced and sold. We need…

Q: 9. We know that 1 ² = n(n+1)(2n+1). Use it to determine the following 26 Σ₁² i=6

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Q: 3.1. Express each of the fol (a). (√2-i) - i(1 -√2i), (b) 2i

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 4. Identify the equation with a constant of proportionality of 8. 2y = 4x 8y = 8x حدد المعادلة التي…

A: Checking each option as shown below

Q: maximize the revenue, how many dresses should be made and sold each week? ( hint r(x) =p(x). Round…

A: Given query is to find the value do x which maximize the revenue.

Q: 1. Suppose a population of insects increases according to the law of exponential growth. There were…

A: Given that the population of insects increase according to exponential model.

Q: (a) Find the derivative. dy=[ y = In(4x - 8) - 3 In(x) (b) Find the derivative. = 1 (²x - ³) State…

A: here we have to find the derivative of function  a) y = ln(4x-8) -3lnx dy/dx = 4/(4x-8) - 3/x dy/dx…

Q: Use the Comparison Test to determine whether the series is convergent or divergent. Σ n = 2 1 n8/9 -…

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Q: For the function f(x) = 2 tan(2x − 2) + 5, find the following. a. The stretching factor: b. The…

A: NOTE: Refresh your page if you can't see any equations. . here coefficient of the tan function is 2…

Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power series…

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Q: d (sin(x) dx cos(x), sec²(x) csc²(x) 2 sin(x)cos(x) cos²(x) cos²(x)-sin²(x) cos²(x) n cosx - simx a…

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Q: Find a Cartesian equation for the curve given by the polar equation r = 4 sin 0. 1. (x - 2)² + y² +…

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Q: The gra Assume MITME a rational all asymptotes and intercepts are shown and that the graph has no…

A: x-intercept: The point at which the graph of the function cut the x-axis.y-intercept: The point at…

Q: i = √ √ 3x² (x³ + 1)²³ dx, w= x³+1 Rewrite the Function in terms of u

A: The objective of the question is evaluate the definite integral and rewriting the integral.

Q: Consider the function f(x) = 12x5 + 30x¹ 300x³ + 4. f(x) has inflection points at (reading from left…

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Q: 7. 3 Let h(x) = ³₂. x-2° (a) (b) Find the inverse, if it exists. Find the domain and range of each.

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Q: 2. Let f(x)= (a) (b) (c) x x+1 and g(x)=2x-1. Find fog and its domain. Find go f and its domain.…

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Q: 3. f-¹(x) = ± √T 4. None of these 5. f¹(x) = √T Find the inverse of f(x) = x7. 1. f(x) = x 7 2.…

A: Given query is to find the inverse of the function.