1)Find the derivative of the following. F(x) = 3x4 – 5x2 + 27)9  2)Find the equation of the tangent to the curve f(x)=(x2+2x+1)4 at the point where x = 3.

Q: y = x³+4x-15 y = x² cos x y=tan(x/3) at x =0 at x=0.4. at x = 3

A: Since you have posted multipart question  i have solved the first three question as per our company…

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A: given

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Q: . For which x value(s) is f(x) = 1 + x x² + 2 continuous? Explain why.

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Q: 2. The function v(t) = t³ - 7t² + 12t, [0,6], is the velocity in m/sec of a particle moving along…

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Q: y=x²² - 2x+1 2 y=5-x²

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Q: Find the critical point(s) for the function ƒ (x,y) = 6x² − 2x³ +3y² +6xy Classify each critical…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 Consider the function f(x) = x + 12x 3 (a) Find the domain of f(x). Note: Use the letter U for…

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Q: Find the average of the function over the given interval. f(x) = x3 − x over [0, 1]

A: The given function is

Q: Use f(x) = x²/3(x - 5) and its derivative f'(x) = 5(x - 2) 3x1/3 to find each of the following. Find…

A: Given that a function f(x) = x2/3(x-5).And we find critical points.

Q: Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the…

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Q: F(x) = Find an antiderivative F(x) of f(x) = 7x - √x.

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Q: Sketch a graph of the function f(0) = 2 sin(-20- - -Зл -5л/2 -2л 0-17) -3/2 -Л +3 -п/2 6 5 4 3 2 1…

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Q: Solve by method of elimination: x' = 3x-y y' = 5x - 3y x(0)=0 y(0)=-1

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Q: 16 x+4 Find the average density Pave (in kg/m) of the rod. The linear density p in a rod 5 m long is…

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Q: Complete the square of the following equation that is in STANDARD form to find the VERTEX form of…

A: given standard form is:

Q: Classify the following conic section from its standard equation: x²-xy-4y²-x-y+4= 0 O Circle O…

A: To classify the conic section from its standard equation:

Q: 1. Consider the function (a) Evaluate the limits x) = -1/2 - 1/1/201 |x| f (x) lim f (x) 110 (b)…

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Q: c and d?

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Q: Assume that the given figure is the graph of f'. AA 1 2 3 4 5 6 Identify the true statements. X f(1)…

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Q: Given F= V(-2-9y¹), find F. dr where C is the quarter of the circle ² + ² = 16 in the fourth Jc…

A: Given so Now

Q: A particle is moving with the given data. Find the position of the particle. a(t) = 11 sin(t) + 8…

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Q: Compute In (9) fhe S 5 e tesx 5x 5 +8 3) ³ dx

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Q: Find the Maclaurin Series for the following function: sin (3x) = = g(x) = sin(3x)

A: The given function

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A: Given : A particle moves in a straight line and has acceleration given by  a(t) = 6t + 4. initial…

Q: Solve using Laplace x" - 4x = 3t transformations x(0) = 0 x'(0) = 0

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Q: Which conic section allows h, k or rto possibly be fractions, the equation is not a rational…

A: Which conic section allows h, k or r to possibly be fractions, the equation is not a rational…

Q: 2. Find the derivative. Simplify as necessary. (a) f(x) = sin x cos x

A: The given function is"Note as per the rules, we are supposed to answer the first question, and rest…

Q: Use the given transformation to evaluate the given integral, where R is the triangular region with…

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Q: = Given that ³-7√x dx = 266 3 what is f¹-7√t dt?

A: Given that a integration and its value and we find the value of reversed integral.

Q: Determine the convergence or divergence of Σ=1 your answer. en 1+e²n and justify

A: The Root Testlimn→∞|an|n=LIf L<1 then ∑n=1∞an is absolutely convergentIf L>1 or…

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Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Consider the function f is defined by f(x) = −2x³ +33x² Find the intervals where the function is…

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Q: Suppose f(x) = (b) Find the average value of f(x) over the interval [3, 15]. Average value= 2 -4 if…

A: The given function is

Q: Determine if the following series are convergent or divergent. Identify which test you used to make…

A: As you posted multiple subparts I need to solve only first three sub parts.

Q: 9x³+4x-2 X dx

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Q: Find your own values from the unit circle that prove that tan(u – v) ‡ tan u – tan v. Show your work…

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Q: Given that 3 Lex ex dx = e³ - e, use this result to evaluate 3 [²Sex + +4 dx.

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Q: Evaluate the integral 1 3 sec²0 6 + 8 tan 0 do

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Q: A car travels down a highway at 50 m/s. An observer stands 250 m from the highway. (a) How fast is…

A: A car travels down a highway at 50 m/s. An observer stands 250m from the highway.

Q: 35. Let R be the region bounded by the following curves. Find the volume of the solid generated when…

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Q: Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) so (70 - 3 csc(0)…

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Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

A: Let a function f( x ) If then function is increasing If then function is decreasing

Q: Choose the correct answer by changing the order of integration of the following iterated integral SS…

A: We need to change the order of integration.

Q: QUESTION 6 Determine the number of triangles with the given parts. a = 34, b = 69, a = 74° 3 2

A: Using cosine rule of triangles, we can find the possible number of solutions.