derivatives

Q: If f(x) = 6 sin- (x), then f'(x) =

A: We have to find solution

Q: 6. Use the definition of the definite integral to evaluate (x - 4) dx. in f(x)dx = lim f(x AX A→0…

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Q: 3) Find the sum of the first 12 terms of the geometric sequence-3,-6,-12,-24,..

A: We can solve as follows

Q: Listen Use the Ratio Test to determine if the series converges or diverges. (2n) Σ 3n(nl)2 n=1…

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Q: ou can compare using the Limit Comparison Test. Then deter 00 1 1 Σ C. and D. 1 n2 n3 n=1 n3/2 n=1…

A: We have to match according to the given information

Q: The future value at 5.25% interest, compounded continuously for 7 years, of the continuous income…

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Q: Use the table of frequently used Taylor series to find the sum of the series. - 3+ 6x - 9x + 12x -…

A: Solution

Q: Express the limit as a definite integral on the given interval. lim Ax, [1, 4] (x;)2 + 3 dx Need…

A: Given query is to write the expression as integral.

Q: Determine the vector equation and the Cartesian equation of the plane tangent to the surface: z =…

A: Here, the given surface is: z=f(x,y)=x3-y3 To find the tangent plane to the surface at a point…

Q: Given the two polar curves, r = 2 sin 0 and r =1- cos? 0, find the following. A) Sketch the graph of…

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Q: Find the area of the parallelogram that has two adjacent sides u = -2i + 4k and v =i +2] +k Axn pu…

A: We will find the cross product and area.

Q: 3. A particle moves along a coordinate axis. Its position at time t (sec) is s(t) = | f (x)dx feet,…

A: answer is in next step

Q: Evaluate the following integral. cos x dx -6x 1 sin 2x dx 2 - 6n O C. dx + cos 2x dx OD. dx + - 6x 6…

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Q: x+3 4.) Evaluate: S x²+5x+6 dx 5.) Evaluate: S xlnx

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Q: If f(x) = [(1³ + 6r² + 1) dt

A: Here, the given function is: f(x)=∫0xt3+6t2+1dt...(1) Note that, the Fundamental Theorem of Calculus…

Q: ermine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

A: Given query is to find the infection point and interval of concave up and down.

Q: @ find dy 3\nx when 2)

A: As per guideline we have to solve one question Please repost other question again

Q: Show that the following functions satisfy Laplace's equation 0. dy? %3D (a) f(r, y) = r*y – xy³

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Q: Find the indefinite integral and check the result by differentiation. COS X 1- Cos x Step 1 First,…

A: Solved below

Q: a) Find the directional derivative of a(r, y) = 3r? - y at (1, 1) in the direction (-3,4).

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Q: A region is enclosed by the equations below. y = 2?, a = 3, y = 0 Find the volume of the solid…

A: We can solve this as follows:

Q: So (xs +x) dx 24.47 %3D The bet ween y = sin x and the x - axis for area

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Q: A graph of y = y = f'(x) over the interval [ - 4, 4]. f(x) is shown. In the same coordinate system,…

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Q: ind the slope of the tangent line to the curve y = V4x – 3 at the point (13, 7).

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Q: 11. (6 points) The demand for a certain product can be modeled using the equation d(x) = x2 - 4x +7.…

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Q: 6. For each function determine: i) the critical values ii) the intervals of increasing or decreasing…

A: 6 A)

Q: Consider the functions. f(u) = u + u g(x) = cos (x) Find the following function and derivatives.…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: How many distinct solutions does the following equation have? I1+I2+I3 +24= 100, such that %3D I E…

A: To find the distinct solution of x1+x2+x3+x4=100 Since, x1∈{1,2,3..},x2∈{2,3,4,…},x3,x4∈{0,1,2,3,…}…

Q: y= f(x) -2- 2 4 8 Evaluate the following integrals by interpreting them in terms of areas: (a) f(x)…

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Q: Test the series for convergence or divergence. 4 6. 8 10 .... 7 8 10 11

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Q: 9. -x² dx Choose the correct graph below. O A. O B.

A: Topic:- application of integration and geometry

Q: For the following table, assume that y = a (x ^b). Then 2 7 9 11 11 17 13 25 y = 3.083 x^2.312 O…

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Q: The variables x and y satisfy the relation 2 = 31-2x. (a) By taking logarithms, show that the graph…

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Q: dr 14. J z(x+1)²

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Q: (Simplify your answer.) (Simplify your answer.)

A: We have to find the value of the given condition  according to the given information

Q: Given r = e-, find the following. A Determine the derivative in terms of 0. Show each step and…

A: First we find dy/dx

Q: te: sec(5 x + 4) tan(5 x + 4) dæ

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Q: Use the Laws of Logarithms to expand the expression. 4x7 In (x + 3)8

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 7 \" 9n2 + 5 00 n =…

A: We have to find out the series convergence test

Q: 1. Under what conditions will a set consisting of a single vector be linearly independent?

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Q: dy when x = 1. dx If y = u" and u= 6x +6, find (Simplify your answer.) dx x= 1

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Q: Evaluate the integral using integration by parts. 5x dx= %xp

A: solving by integration by parts

Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx² + 5x3 –x-3…

A: Given problem:-

Q: 5) Find the value of the infinite geometric series. a) 500 - 100 + 20- 4+...

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Q: 4) Find the sum =1 an for the geometric sequence an = 10 - 3 %3D

A: The geometric sequence, an=10.3n-1

Q: A region is enclosed by the equations below. y = 8, 3 x = 1 z + 4' Find the volume of the solid…

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Q: Simplify the following expression. dt dx 2+1 dt .2 dx t +1 0.

A: In the given problem first we integrate the given integrand and  then differentiate the integral .

Q: Find the equation of the tangent line for f (x) = 2 sec(z) at z = 6

A: To find out the equation of tangent line.

Q: g(x)dx% = %3D (Simplify your answer.

A: