|*| +1, {0, x = 0 1x-1, x >0

Q: Find the derivative of the following functions from first principles. (i) x? (ii) e (iii) log (x +…

A: derivative

Q: | (6x – 3* dx = / (бх f(u) du where u = (enter a function of x) dx (enter a function of x) = np a =…

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Q: d y Find dx? |(-1,2) if x² + y' = 9

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Q: DSk = 4x +C = 4x

A: here ?∫ dx = 4x + c now we can differentiate both side so we get the function f(x) = 4 so here…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: I am attaching image so that you understand each and every step.

Q: 4. If s t-5t2 + 5t - 3, the velocity is equal to 2 if t =,

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Q: The shape of the Gateway Arch in St. Louis is approximately a parabola with a base and a height…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: dy 1+ y+1

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Q: (5x) сos (Зa')dx COS

A: LetI=∫cos5xcos3xdxI=12∫2cos5xcos3xdxWe know…

Q: Which of the following gives the formula for the inverse of the function x + 3 f : R \ {-7/2} → R \…

A: I am attaching image so that you understand each and every step.

Q: Which of the following is not a possible zero off(x) =2x-5x+ 127 03 5 3

A: Given

Q: |(x + 1)°sinx dx -(x + 1)³ cos x + 3 (x + 1)² sin x – 6 (x + 1)cosx – 6 sinx + C (x + 1)³ cos x – 3…

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Q: 7.5 Identify the marked points as being an absolute maximum or minimum, a relative maximum or…

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Q: dy cos x + (sin æ) y = 9 dx y = 9 sec - C cos æ y = 9 sin a ++ C cos x y = 9 sin? x + C cos æ y = 9…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Find your answer below

Q: Q4. The following set of data represents the number of families (n) moving into a new town as a…

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Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: 5. Evaluate the indefinite integral, ſ' coth- dx. - 6.

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Q: Find dy for the given values of x and dx. y = x + x2,x = 4, dx = 0.02 %3D %3D

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: find the tangent to the curve f(x)e%*-2% at X=-1. Express answer exactly in terms of e (not a…

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Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: Use seperation of variable to solve the following differential equation (DE): (11 + x) dy – y dx = 0…

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Q: 9. cos(x-)

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Q: Evaluate/Find the following integrals. dx 3. S. 3 1+ x

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Q: 5-(1+x')(dy-dx)= 2.xydx;

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Q: Solve the differential equation with appropriate method. Finalize answer free of fractions and…

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Q: Sove the following continnity queshans below Let f(x.y) = 2xy? f (xiy) = (0,0) nd Let glan)= f fary)…

A: here we use the simultaneous limit definition and arbitrary path choosing that passes through the…

Q: v=(5,1,-2), w=(4,-4,3) find the angle of 0 between the vectors v and w.

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Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Find the derivative of the following functions from first principles. (i) x? (ii) e* (iii) log (x+…

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Q: 3. y = tan (3x)cot (3x)

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Q: A box with a square base and open top must have a volume of 4000 cm. Find the dimensions of the box…

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Q: 22. Which of the following statements about the functions y = f(x) and y f(x) is true? A. If the…

A: Here, to find the correct statement for the functions y=f(x),y=1f(x)

Q: Use vectors to determine whether the points are collinear. (0, –2, –5), (10, 13, 15), (4, 4, 3) The…

A: The given points are,      0,-2,-5, 10, 13, 15, 4, 4, 3

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is a(x) =…

A: Use the basic concepts of the average and marginal costs.

Q: A culture initially has 700 number of bacteria. At 1=5 hour the number of bacteria is measured to be…

A: The differential equation that describes the given model can be solved by using the variable…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Determine the area, in square units, bounded above by f(r) = x2 + 10x + 25 and g(x) = -x +1 and…

A: Topic = Area The area is 323.

Q: Suppose that it is given to you that f′(x)=(x+5)(10−x)(15−x) 1.The first inflection point (from…

A: Given that,     f'(x)=x+510-x15-x

Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

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Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: Find the (natural) domain of the function x + 1 2х — 1 f (x) = Select one: a. (-0, –1] U (1/2, ∞) b.…

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Q: pleasee answer C and E

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Q: Applications of Integral calculus 3. The following curves bounds a certain area: y = 4x – x2

A: Area bounded by a curve y=f(x) on [a,b] is given by, A= ∫abydx