Problem 6. Find a function f(x) whose derivative is f'(x) = x²√√√x³−1+x³ and which satisfies f(2)= 1.

Q: 2x Eliminate the arbitrary constants of y=x²+c₁e²x+c₂e 2 3x

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Q: For what value of a is the following function continuous at every x? a²x-6a, x≥2 x<2 f(x)= 20,…

A: Given fx=a2x-6a20x≥2x&lt;2

Q: 1. y=√√3x²-5x+

A: Given: y=3x2-5x+1

Q: Find the area of the surface generated by revolving the given curve about the y-axis. y = √36x², -5…

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Q: Evaluate the integral. x+7 2 x² +64 dx

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Q: ← Find the average value of the function f(x)=x²-23 on [0,9]. The average value of the function…

A: To find average value of the function.

Q: K Suppose that lim f(x) = 13 and lim g(x) = - 10. Find the following limits. X-6 X-6 a. lim…

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Q: The hyperbolic tangent and secant are defined as sinh tanha cosh a 1 cosh a sech a Find the…

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Q: Given f(x) = cotx 1 - csc x " then f'(x) = = 1 g(x) - 1 Find g(x).

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Q: function of x and y sın (x²₂ + y²)+2x³=yz²+2, If z is a differentiable satisfying the equation find…

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Q: Given f(x) = a) f'(x) b) f'(1) = [ = 2x² tan x sec x > answer the following:

A: The function is given by fx = 2x2tanxsecx To evaluate: The expression of f'x and the value of f'1

Q: 3. Use algebra to calculate the limits in parts (a) and (b) exactly, giving your answers as exact…

A: Given :(a) limx→4x2+2b limx→-3x2-x-1211x+33(c) limh→0h+16-4hd limx→0+xx

Q: x² - 3x Find lim x→3 x2 - 9 2

A: to find out the limit.

Q: Problem 8. (a) Je* sin (2) (b) ) [(x +3 (c) [²² +3) In (x) dx (In (x))² dx Calculate each of the…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: (1) Given f(x)=2x+√x, find (ƒ-¹) (3)

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Q: Solve the inequality 6x^2+5x<4 Please show on a

A: Given Inequality:- 6x2+5x&lt;4

Q: Find the solution of the given DE. 10. +2²=2y√x

A: To find the solution of the given DE.dxdy+2xy=2yx

Q: K Find lim h-0 f(x+h)-f(x) h f(x) = -8x-7, x=2 The lim f(x+h)-f(x) h for the given function and…

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Q: Calculate the scalar triple product u (v x w), where u = (1,5, 0), v = (-8, -9,9), and w= = (4,…

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Q: f f(x) I = 1 √3x + 1 f(3+h)-f(3) h find and simplify the quantity |

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Q: Find the derivative of the function g(x) = sinx - xcosx, and show work.

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Q: A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine…

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Q: A certain bacteria culture is known to grown at a rate proportional to the number of bacteria…

A: let   p=amount of bacteria present   thendpdt=growth rate

Q: 5. For the constant numbers a and b, use the substitution = a cos² u + b sin² u, for 0 <u<, to show…

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Q: Calculate the first, second, and third derivatives of y(x) = x-19/5 (Use symbolic notation and…

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Q: Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the…

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Q: direction: find the indefinite integeal   x-3  / x^2 + 1

A: Given query is to find the integral.

Q: f you know that lim f(x) exists at an interior point of a domain interval of f, can you find its…

A: Limit of a function.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Derive the following functions 38. y=(x²-2x+5)(x²+2x+5)…

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Q: Find the equation of the tangent plane to the surface f(x, y) = x² + y² at point (3, 2, 13). 6x + 4y…

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Q: 8) Given two planes P₁:2x+4y+3z=4 and P₂:x-y-2z=-3 (a) Let L be the line of intersection of the two…

A: Given Planes :- P1: 2x+4y+3z=4 P2: x-y-2z=-3

Q: Find the following limit. lim X-0.25 lim x--0.25 x+9 x+2 x+9 x+2

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Q: 11. The Australian Teal Frog is a species that has become endangered due to inability to defend…

A: As per Bartleby guidelines we only give first three questions answers. Please repost for other…

Q: 14.5y² + y-6 15. 2r-r-3 16. 3m² + 7m + 2 17.3y² + 14y +8 18. 8v² + 13v - 6

A: Since you have posted multiple questions, we are supposed to only first three questions. If you want…

Q: The graphs of 2 = 8, y = g(z) (solid) and y=h(z) (dashed) are shown; the graph is not drawn to…

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Q: Given the demand equation p+ = 48, where p represents the price in dollars and x the number of…

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Q: 16. (x − y ln y + y ln x) dx + x(ln y − ln x) dy = 0.

A: The given differential equation is; (x-ylny+ylnx)dx+x(lny-lnx)dy=0

Q: ladder 12 feet long is leaning against the wall of a house. The base of the ladder is pushed towards…

A: Given query is to find the rate of change of top of the ladder.

Q: Let D = {-4, √6, 0, 2, 6.5, 10, 0.4, n}. Which elements of D are real numbers? (Select all that…

A: Real number:-It called father of number because it contain all numbers i.e it contains rational ,…

Q: Determine f-¹(x). ƒ¯¹(x) = = -x² + 16x What is the domain of ƒ-¹(x)? What is the range of ƒ−¹(x)?||…

A: P

Q: A certain bacteria culture is known to grown at a rate proportional to the number of bacteria…

A: Substitution and calculation is the key for such problems.

Q: 10. The national debt of a South American country t years from now is predicted to be D(t): 65 +9t3…

A: Topic- Application of derivatives We are given, Predicted nationl debt of a South American country t…

Q: 54. P(x)= x³ + 2x²-3x - 10, 55. P(x) = 2x³ + 7x² + 6x - 5, 56. P(x) = x + 3x³ c = 2 c = } 16x²27x +…

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Q: Find the solution of the given DE. 7. +q=4 cos 2r; q(0)=1. dt

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Q: Consider the following functions. f(x) = ²/₁ g(x) = 3x + 12 Find (fog)(x).

A: Given: f(x)=3x       gx=3x+12

Q: f(x) is graphed below. Find each value. 10+ 9 8 7- 10-9-8-7-6-5-4 f(x) = lim 2115 lim f(x) = lim…

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Q: 6) Given x²-4y²-16z² = 4 (a) Rewrite into standard form and name/identify the type of surface. (b)…

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Q: A hazardous material was found to decay at a rate proportional to the amount present. Initially,…

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Q: 25. (y + √√x² + y²) dx − x dy = 0; when x = √√√3, y = 1. ANS. x² = 2y + 1.

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Q: plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 35,000…

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