4. Given f(x) = x² +3 and g(x) = -3x + 11, find the following a. f(g(3))

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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Q: 2. What is the average rate of change from x = 4 to 9 of f(x) = 200e-03x

A: We need to find average rate of change.

Q: Solve the differential equation. y' + 2xy = 23x A There is no correct answer from among the given…

A: To solve the differential equation. y'+2xy=23x

Q: Simplify the following: 5 2 + x² + 5x + 6 x² + 4x +3

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Q: Evaluate t9e²t5 dt.

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Use the Intermediate Value Theorem to show that the following equation has at least one nonzero…

A: Given That,  Sec(2x)= 3^x

Q: 14. Evaluate to 4 decimal places: csc 153°

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Q: Label the zeros and asymptotes. Graph each function. Answer each limit question. 11. f(x) =…

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Q: Solve the following linear system by Gaussian elimination. X1 = X2 11 x3 = and X1 + 4x2 + 2x3 = 12…

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Q: Let u(t)=9t³i + (t²-1)j- 4k. Compute the derivative of the following function. u (tª - 2t) Select…

A: Apply the derivative for the function as given in the question.

Q: The point P(1, 0) lies on the curve y = sin( (a) If Q is the point (x, sin(¹3″ )), find the slope of…

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Q: Solve the given differential equation. All solutions should be found. 3x² - 3y - y³ 3x + 3xy² dy dx…

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Q: OE OF OA OB Ос OD The only horizontal asymptote of f(x) = A)y=0 E) y = In (3) B) y = 1 F) None In…

A: To determine the only horizontal asymptote of fx=lnxx.

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

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Q: If an investment decreases 1% the first year, 6% the second year and 9% the third year, what is the…

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Q: у=х+5 6х

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Q: Determine whether the three points are collinear. (0,-4), (-3,-6), (2,-2) Are the three points…

A: See this solution in below with details

Q: 6 y² +9' represents the volume of the solid of revolution formed by rotating Q about the x-axis?…

A: Here we have to choose the correct option.

Q: If f¹ f(x) dx = 3 and 5 f¹ f(x) dx = 25, then ff(x) dx A)-2 B)1 C)-1 D) 2 E) 8

A: We have ∫3-1f(x)dx=3, 5∫31f(x)dx=25  We have to find ∫-11f(x)dx=?

Q: The family of circles with center on the line y = 3. A B Ⓒ D 1+ (y − 3) y ''+ (y') ²=0 1+ (y - 3)…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Find the area of the region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

Q: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

Q: 10. If h(x)=x-3 and g(x)= x. Find (hg)(x)

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Q: Non-exacr or first order linear DE

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Q: Eliminate the arbitrary constant. 2x -X y=c₁e + c e 1 2 A B с D y" y'- 2x=0 y"-y'- 2y=0 2y"-y-2x=0…

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Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

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Q: A company produces a special new type of TV. The company has fixed costs of $497,000, and it costs…

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Q: 6. Write the following power functions in the form f(x) = kx² a. f(x) = -³/3 x3 b. f(x) = ³² c.…

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Q: What is the coordinates of the point on the line y = 2x +1 which is closest to the point (2, 1)?

A: The point on the line y=2x+1 which is closest to point (2, 1) is the point through which a line…

Q: The following questions should be completed and your answers brought to class. Spending on Baseball…

A: Given graph: The given graph is a bar graph. In bar graph, height or length of the bars are…

Q: 8. (a) Compute the roots of the quadratic polynomial s² + 2s + 5. (b) Is the polynomial s2 + 2s +5…

A: Given quadratic polynomials2+2s+5a.Discriminant,D=b2-4acD=22-4×1×5D=-16D&lt;0so, this quadratic…

Q: 15. f(x)=2x²(x+3) (x-2) a. b. C f(x)= 16.

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Q: 6. Let [√16-X² Find y(2√3) 16-x? 2 16

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Q: 1. The slope of the perpendicular line 3x+6y=2 is a. m' = 2 b. m² d. m' = -2 m' = 2 2. The equation…

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Q: The differential equation dy 18 dx y¹/2 + 4x²y¹/2 has an implicit general solution of the form F(x,…

A: The given differential equation,      dydx=18y12+4x2y12 we have to find the general solution of the…

Q: Write 11 Stan¹¹ iftan x dx in terms of 9 tan x dx

A: The integration of tan11x write in terms of tan9x.

Q: b. lim X-C * 17 x c where c is some fixed real number.

A: Above question is solved.

Q: - In 8 e³ -5 ln(

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Q: Need this in complete and handwritten solution, thank you! 3. Solve for the Homogenous Differential…

A: Ode

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Q: Solve the Differential Equation x² (y² +3) y(x³+1) dy + dx = 0

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Q: The following table gives the number II(t), in millions, of adult Americans with Internet access in…

A: NOTE: Refresh your page if you can't see any equations. . t 2000 2003 2009 I 101 160 190 .…

Q: 9. Let f(x) = 4x² - 2x, 2 √3x- x - 6, 2, Find a) f(-1) b) f(3) c) f (8) d) f(1) e) f (6) x ≤ 1 1<x<…

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Q: The rate of change of the variable y with respect to x is equal to the expression 5x*-3e***. What is…

A: rate of change of variable y with respect to x is =dydx

Q: 1. Solve the differential equation xy dx = (x+2) dy =o

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Q: Using the definition of a derivative, find s'(x) given s(x) = -x² - 2x + 3. Do not include s'(x) in…

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Q: Let ˜(x)=3e³x (10−6x)+e³* (−6) Find the value of x that makes f(x) = 0 Pick test values and plug in…

A: Topic:- function

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A: