1. Find the derivatives of the following functions. Hint: use logarithmic differentiation (take the natural log of both sides to start), then use implicit differentiation and solve for dx' substituting in as necessary to reach an answer that only contains the variable x. dy a) y = (x² - 1)Inx

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Q: eliminate arbitrary constant Ae^3x+Be^4x+Cxe^3x

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Q: a lim x³²-x² X→ I X-1 b) lim X- UT 5 4-1 (2x-1) (3x²+2x-7)(x²³-9x)

A: SOLUTION-

Q: 4. Find the solution of the IVP y" – 4y' — 12y = 3e5x, y(0) = 18 7' y' (0) = -1/₁

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Q: 3. Determine if the following functions are one-one. Explain why. •f: R R f(x) = (x - 2)² ● f:R R…

A: one- one function :Let f be a function which is one one if        x1≠x2   ⇒  f(x1) ≠ fx2 for every…

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A: NOTE: Refresh your page if you can't see any equations. . take the derivative

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Q: d (/X-31+4) dy SC

A: Given query is to find the the derivative of the function.

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A: see below the answer and explanation

Q: (a) y 10u² and u = 5 - ² (b) y = √u and u=1-1

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A: Given, C(x)=3x-82x+9

Q: 3. h(x) = 4x² + 4x + 3;h(x) = 0

A: Explanation of the answer is as follows

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A: Topic = Algebra

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A: On solving this we will get :      Option (5)  is correct

Q: (d) y = e ln(x² + 2) (e) y=e5³ (f) y = 2x¹e-z

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Q: Find the volume of the solid generated by revolving the region about the line x = 2. The region…

A: volume=16.75 unit cube

Q: Consider the function: f(x) = 2x² – 2x – 1 Recall that the definition of the derivative is: f(x…

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A: Given the DE is y''+4y'+4y=0.

Q: ey (x + 1) = ex

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A: Topic:- calculus

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A: Given :- ∫01∫0y2fx,ydxdy+∫1e∫lny1fx,ydxdy

Q: Three regions are defined in the figure. C (0,2 y R₂ /y = 2√√x R3 y = 2x R1 B(1, 2) A (1,0) X Find…

A: Here,                we have given a region R1 now if this region is rotated about the line OA we…

Q: Given U₁ = = 0 (93).- (3). = - (²) (₂). 0₁ = = (-²) U4 , V3 = peform the indicated operations

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Q: 10. Suppose for a differentiable function g(x), we have X g'(x) = ( − 3)³ (5x – 6). Identify and…

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Q: 2y+9x² find all -2x-1' coordinate points on the curve where X x = -1 and the line tangent to the…

A: solution is given below.. one point lie on curve at which slope of tangent line is 1.

Q: Find the (linear) equation of the tangent plane to the surface z=xexy at the point (7,0,7). Your…

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Q: d³y 1) Find the order and degree of the differential equation: + dx³ 3d¹y dx4 = dy 4xy dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the gradient of f(x,y,z)=xyz2. ∇f=_______ i+___________ j+______________ k

A: Given, f(x,y,z)=xyz2

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Q: Descartes' Rule of Signs to determine the possible number of positive and negative real zeros. Be…

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Q: Find the average value fave of the function f on the given interval f(x)=√x, [0, 16]

A: To find the average value fave of the function f on the given interval.  fx=x, 0, 16

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A: The function is given as , gx=e-x4 , -2≤x≤1 Find the absolute maxima and minima values. Then graph…

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Q: 34. A force of 6 pounds compresses a 16-inch spring 4 inches. How much work is done in compressing…

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Q: An open-top box is to be constructed from a sheet of tin that measures 18 inches by 12 inches by…

A: Volume of a rectangular box of length l, width w and height h is given by  V=l×w×h.

Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: Find the GS of y" - 4y' + 5y = 0

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Q: •ffe -32²-3y² dA; R= {(x, y)\x² + y² ≤ 4, x ≤ 0,y>0} R 4. (Section 16.3) Evaluate

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