Given that f(x) = 9x + x³ + 6, find the derivative of f- by using dy the formula dx 1 Check your result by differentiating implicitly. dx dy (f-1)'(y)

Q: Let y(x) be the solution to the following initial value problem. dy (In x) y(1) = 1 dx x y? Find y(e...

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Q: Given a function whose graph is shown below. The function is continuous on[1,3]. Always True 1. O So...

A: The given graph shows that - The given function has a non removable discontinuity at x= 2 ( Non remo...

Q: f sufficient condition e necessasy & V= constant to be comsteant gedesic on EE, +FE, - a EF, = 0 a) ...

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Q: 3. Construct an angle of 65° from two straight lines and bisect the angle.

A: Construct an angle of 65 measure at O using protractor

Q: Skx², (2x + k, x 2 f(x)

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Q: csc5x cot5x dx A csc 5x B -csc5x 3 -csc5x 3 D csc5x E None

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Q: In each case, determine whether or not the lines have a single point of intersection. If they do, gi...

A: (b) r1 = <4t, -3t+1, t-4> and r2 = <2t-3, -t, -t-1> So, if they have a point of intersec...

Q: Bessel's Function Find Jg (x), JE cx)

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Q: Find the extreme values of f (x, y, z) = x + 2y subject to both constraints x + y + z = 1 and y? + z...

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Q: dy x + y ; 4- dx 2xy ls

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Q: 00 Does the seriesE 1 converge or diverge? Give a reason for your answer. 15n - 1 n=1

A: 1P- Series Test:The series ∑1np = 11p + 12p + 13p + ...1. Covergent if p>12.Divergent if p≤12 Com...

Q: 00 k k +1 k=0

A: Leibnitz's test: Let ukk∈Nbe a monotonic decreasing sequence such that limk→∞uk=0 Then the series ∑k...

Q: If f(r) is positive then for all 1 <I<2, we have So f(z) dz 7. Select one: O True O False

A: If f(x) is positive then for all 1≤x≤2, we have ∫07f(x) dx≥7

Q: dx 2+x?

A: Given, ∫dx2+x2 We have to integrate it.  

Q: sec ~dx 3 In sec - + tan- +C 3 3 3 A True B False

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Q: The population of Hungary1 has been modeled by P=9.919(0.998)t, where P is in millions and t is i...

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Q: Evaluate the function for the indicated values. f(x) = 6|||| + 3 (a) f(0) (b) f(-2.8) (c) f(4) (d) F...

A: f(x)=6x+3a) For x=0f(0)=60+3f(0)=6(0)+3f(0)=3b) For x=-2.8f(-2.8)=6-2.8+3f(-2.8)=6[2.8]+3f(-2.8)=6(2...

Q: 1. Determine whether the series converges using any appropriate test. Identify the test for converge...

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Q: Changing the catesian to polar coordinate.

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Q: Which of the following series converges and which diverges? Find the sum of the convergent series. 0...

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Q: Eind equatons of the following x²-2y²+2²+ yz =20, [4,6-3) W the tangent plane 6 the normal line to t...

A: Solution: f(x)=x2-2y2+z2+yz-20

Q: Evaluate. 3 If f(2)dz = and 9(=)dz = - 1 what is the value of g(x)dx [6f(x) + 29(z)]dz =?

A: Topic = Integration

Q: 1 Find lim 3 s-2- \s-2 s²–4,

A: Given, Evaluate lims→2-1s-2-3s2-4

Q: х-2 Determine lim x→2- 2-V4x-x2 Your answer

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Q: The integral dx is Select one: O None. o o o

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Q: For a continuous function f(x) on the set 2 [- 5,2], the net area Tx)dx must be -5 always positive S...

A: The given question has been solved in detail

Q: At what point is the tangent line to the curve y = 6x² perpendicular to the line x + 2y – 8 = 0? NOT...

A: Follow next step

Q: The function f(x) = 2a – 392? + 240x – 4 has two critical numbers. The smaller one is x = and the la...

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. (Hint: factor the den...

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Q: If f(x) = a +2a + 4, then the estimation of the area under the curve y = f(x) between 1 <r < 2 with ...

A: We have to choose correct option

Q: 100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the ro...

A: Theorem : If the series ∑n=1∞|an| converges, then the series ∑n=1∞an also converges.                ...

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3< ...

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: Use the integration by substitution to find the integral –6x² – 4 dx . (7³ + 2x)²

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Q: -2 The function graphed above is decreasing on the interval The inflection point is at x = on 2-

A: Solution: Clearly by graph we can observe that  

Q: Select ALL possible answers. Which of the following statement/s is/are true of the function whose gr...

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Q: To evaluate Je ?" sin(e²^) cos(e²«) dx, we let u=e A True B) False

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Q: Use Simpson's Rule with n = 4 steps to estimate the integral. (Hint: if you calculate using decimals...

A: The integral is  ∫13 9x2dx

Q: Suppose a consumer lives in two periods, with his income in period 1 as $100 and his income in perio...

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Q: TRUE or FALSE. Type in "1" if TRUE, type in "2" if otherwise. | f(x)dæ = F(x) implies that d [F(x)] ...

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Q: Evaluate dw using the given information. 5x? + 4y? w = -; x= - 5, y= 3, z = 1, dx= 0.01, dy = - 0.08...

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Q: dy Use implicit differentiation to find if tan'(ry + y) = x. dx dy dx

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Q: kdt, where k is constant k A True B) False

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Q: The table below gives the percentage, P, of households with a VCR, as a function of year. Year 1978 ...

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Q: Find a domain on which f(x) = (x −3)2 is one-to-one and non-decreasing, then find the inverse of f r...

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Q: lirectly using the calculator, compute the zero- through fourth-order approximation of v7. For each ...

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Q: dy Find dx if y = x (log2(x* – 4x))° dy dx ||

A: Topic = Derivative

Q: Determine if the sequence {a,} converges or diverges. Find the limit if the sequence converges. (- 1...

A: Here we have to determine whether the sequence {an} converges or diverges.

Q: The direction field for the differential equation dy = e*-y dx passes through the point y(-1) = 2 is...

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Q: Is the function f (x) below continuous on [3,+0)? (0, x > 0 X, 0 3 Choose

A: This question is related to limit and continuity, we will solve it using given information. 

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5, ...

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)