If f(x)= = 3x5 – 5x4 – 3x³ x4 " find f'(x).

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Q: Set up the definite integral required to find the area of the region between the graph of y = 16 -…

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Q: Determine Duf (3,-10) for F(X, Y, Z) = 4x - y² ³ 2 3x2 of ✓² = (-1₁4, 2) in the direction

A: Given function have to find the directional derivative in the direction of vector .As we know -

Q: What is the distance between the given planes? P1: z= x + 2y + 1 P2: 3x + 6y - 3z = 4

A: To solve the given problem:

Q: Find the local linear approximation of f(x) NOTE: Give your answer in terms of x and not Ax. 1 √1+x…

A: we need to find out the linear approximation of the given function at the given point."Note that as…

Q: Consider (V xF) · nds S where F = 6ex² + y²i + 7e=³j+ln(z+13)xcos y k and S is the top half (≥ 0) of…

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Q: 6. Identify the key points and coordinates (center, vertices, covertices, foci, transverse axis and…

A: The given equation of hyperbola is

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: 3a If f(x) is continuous and ſ³ª f(x)dx = 496.8, what is a [" Round your answer to two decimal…

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Q: What present value amounts to $368,302.35 if it is invested for 4 years at 21% compounded…

A: Given, final value= $368302.35.Given, rate= 21%.Given, time= 4 years.Formula for compounding…

Q: Let f(x) = (x-3)-2. Find all values of c in (2,5) such that f(5)-f(2) = f'(c)(5-2). (Enter your…

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Q: Find the derivative of the function. y' = X ¹ ( 132 a y = tan-1 + In x + a х-а

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Q: Let f(z) = 10 +4-15e*. Find the equation of the tangent line to the graph of f(x) at the point (0,…

A: The function is The point on the graph of  at which the tangent line equation needs to be determined…

Q: Use a linear approximation (or differentials) (32.03) 4/5 estimate the given number. (Round your…

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Q: 2. (a) Find the slope of the tangent line to the curve f(x) = 2x³ - 3x at x = -1 using a definition…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the smallest number n of terms needed to obtain an x 9 approximation of the series accurate to…

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Q: lim ←x sin²x x- x - 13 ㅠ 311

A: For the following limit, to find a number  and a function  such that thelimit equals .

Q: / 2 - 100% + A A particle moves according to the equation of motion s = t5 - 10t³ + 18t, where s…

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Q: The definite integral: Use geometry to find (2+√9-x²)dx. a.

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Q: How long will it take to double an investment at 5.3% compounded continuously? Round your answer to…

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Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the 2 conic section x² -…

A: To find the center, foci, vertices, asymptotes, and radius, as appropriate, of the following conic…

Q: Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

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Q: The population of Vero Beach can be modeled by the function P = 17234e0.01921t where t is the number…

A: where t is the number of years since 2020

Q: Σın k=1 k + 1 k

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Q: (b) logą (3x - 5) = 4

A: The given equation .The aim is to solve the equation.

Q: Compute the derivative of the following function. f(x) = 5xe-5x f'(x) =

A: we need to find out the derivative of the given function.

Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

A: The given function is

Q: A manufacturer has been selling 1600 television sets a week at $390 each. A market survey indicates…

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Q: Find the derivative of the function at P0 in the direction of u. f(x,y)=4x2+3y, P0(7,10), u=3i-4j

A: f(x,y)=4x2+3y, P0(7,10), u=3i-4j

Q: Using the given graph of the function f, find the following. (a) the intercepts, if any (b) its…

A: we are given the graph and we need to find out the x-intercepts, y-intercepts, domain, range, and…

Q: Find the following derivatives. z and Z₁, where z = 6xy - 4x²y, x = 5s + t, and y = 5s - t Zs (Type…

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Q: Find the area of the following region. The region inside one leaf of the rose r = 8 cos (30) The…

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Q: 11. A conical water tank with a vertex angle of 60° is being filled with water at a constant rate of…

A: Let r be the radius of the water surface and h be the height of the water inside the cone at any…

Q: which they occur. f(x) = 4x+7; [-5,5] The absolute maximum value is at x = (Use a comma to separate…

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Q: Evaluate the definite Integral S 3 dx ~ (x² + a)

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Q: Determine if any of the lines are parallel or identical. L₁: x= 6-3t, y = -2 + 2t, z = 5 + 4t L2: x…

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Q: Use logarithmic differentiation to find the derivative of the function. cos(x) y = sin(x)

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Q: Write a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer…

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Q: point at which the line f(x) = -5x - 16 interse

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Q: 2. Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water…

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Q: Find the derivative of the function y = ef In(52) writing the answer in factored form:

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Q: Use algebra to find the point at which the line k(z) = 33 10 3 f(x) = = x + 35 Y ===- Write the…

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Q: Find the length of the spiral r=0², 0≤0≤√21. The length of the spiral is (Simplify your

A: Consider the curve

Q: Consider the following equation. x²7xy-y²-5y = -47

A: x2−7xy−y2−5y=−47

Q: Ihd an equation of the line tangent to the curve y = An equation of the tangent line is 5x 2 x +4 at…

A: Here we will solve it on finding the slope at x=4 after that we will use the formula of equation of…

Q: 4. A weather balloon rising from the ground at 120 ft/min is tracked by a range finder located 350…

A: A weather balloon rising from the ground at 120 ft/min is tracked by a range finder located 350 feet…

Q: Evaluate and simplify y'. 5x²-9x 2 3x+4 y=- y'=0

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Q: True or false: For any real number b > 1, and any real numbers > 0 and y > 0, it must be true that:…

A: Yes, the statement logb(xy)=logb ​(x)+logb ​(y) is true for any real number b>>1 and any real…

Q: Find explicit formulas for sequences of the form a1, a2, a3, . . . with the initial terms given…

A: Given that the sequenceAnd  To find the nth terms