(a) -r -8x – 15 < 0 (b) r – r² > 5(x³ – x) > 5(x³ – r)

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

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Q: 1. Use the 8 step algorithm for curve sketching to analyze the key features of the following functio...

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Q: The derivative of the function y = ecos²(x) is: y' = - sin(2x)eCos² (x) y' = sin(2x)eCos²(x) the abo...

A: We will find the derivatives of the given function y=ecos2x in the following step.

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Q: If f(x) = 6 cot-lx+ 8, then find the value of f'(-2) is %3D 6.

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Q: Let w = xey/z, where x = t², y = 1-t, and z = 1+ 2t. Use the chain rule to find X. (Write your answe...

A: Given query is to find the derivative.

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Š(- 1)*+'6 k! ...

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Q: 1. sin

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A: We need to find average sales in % weeks.

Q: Exercises: Find the general solution of the following differential equations 4) y"+2y'+y=3e*

A: Given

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A: Use the derivative of the form y = u.v

Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

A:

Q: dy dr 2° y0- 13 is Find using implicit differentiation, for the equation - O O O O

A:

Q: d) f(x) = e) р(х) %3D (е* + 1)(е* — 1) x3

A: Given: To find derivative of  d) f(x)=exx3 e) p(x)=(ex+1)(ex-1)

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A:

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

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Q: Vhich of the following best describes the function below? S (x) = * -4 ifx<2 |Vx-2 if 2sx A. Continu...

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Q: Evaluate: sin ycos ydy. sinºy A siny +C 8. 6. sin y sinsy + C 8. sin°y sin'y + C 8. - 6. sin'y + C 8...

A: Here we need to solve the given integral .  

Q: The derivative of the function y = cot¬1(csc x) is: csc x cotx cSC X cot x y' y' = csc?x+1 csc?x+1 t...

A: See the details solution in below

Q: Select ALL possible answers if there is more than one. (3-2x ifx<2 [3x-7 if 2sx' Which of the follow...

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Q: Q2 a. Solve the nonhomogeneous differential equation: y" -5y" -6y' = 3e2*

A: The given differential equation is : y"'-5y''-6y'=3e2x. Repost the next part. 

Q: Cansider the function. x) - 3x - 8 And the Inverse function of r. Slep 1 Let y- 3r-8, then solve or ...

A: The given function is; f(x)=3x-8.

Q: 5. arcsin 1

A: Solution ) arcsin1 = sin-1(1) [ Sin (π/2) = 1 ] Sin-1(sin(π/2) ) =π /2 Or in radian = 1.5714

Q: 5. Determine the slope of the tangent at point (1,5) on the graph of f(x) = (9 – x²)} + 1.

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Q: Q14

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Q: Use any method to determine whether the series converges or diverges. 00 1 Σ 2 + 7-k k=1 O The serie...

A: Given query is to find series converges or diverges.

Q: Use integration by parts to evaluate the integral: for 9t sin(t)dt

A:

Q: az az Find and e = 5x 2² + sin(r + 2) – y?.

A: Find the partial derivative of z with respect to x and with respect to y respectively

Q: Use a linear approximation to estimate the following quantity. Choose a value of a to produce a smal...

A:

Q: S cos?x-ex

A:

Q: g3 (*° – 2x² + 1)dx 9. Evaluate the definite integrals (give exact answers): •3 a) | (2x+3)(x – 5)dx...

A: Given that, There are two integral given, a). ∫23(2x+3)(x-5)dx b). ∫121x3(x3-2x2+1)dx We have to fin...

Q: x2 – 1 dx 9х3 — х

A:

Q: Using an appropriate substitution, gtan-1 x the integral S dx equals: 1+x2 gtan-1x + C 4 tan-1x + C ...

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Q: alculate the curvature of the vector function when t=0.1: 7(t) = (e", V2t, et)

A:

Q: The solution of the non-exact differential equation y dx + (3 + 3x – y)dy = 0 is: O (y^3) (1+x)-(y^4...

A: This question can be solved using the concept of linear differential equation.

Q: Evaluate: ,(3y – 8y* + 9y²)dy | -2

A: let I = ∫-223y6-8y4+9y2dywe know that ∫-aaf(t)dt = 2∫0af(t)dt

Q: Find the values of a and b if the tangent to y = ax² + bx at (1,5) has a slope of 8.

A: We can find the value of a and b as below

Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)...

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Q: Using an appropriate substitution, (cos-1 (x) the integral S dx equals: V1-x2 -e(cos- (x) -elcos-1(-...

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Q: Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the -axis...

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Q: 5x + 400 A garden shop determines the demand function q = D(x) = during early summer for tomato plan...

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Q: Find  dy du,  du dx, and  dy dx. y = 2   u,     u = 5x + 3

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Q: Suppose that f(x, y) and the region D is given by {(r, y) | 1 < # < 2,1 < y < 4}. D Then the double ...

A: ∫∫D f(x,y) dx dy = ∫y1y2∫x1x2 f(x,y) dx dy

Q: 1. dx+ e*dy=0 5. x(1- y)dx+(x² -2)dy= 0 5. sin2xdx+4ycos² 2xdy=0 dy_ xy+3x-y-3 dx xy-2x+4y-8 . (4y+ ...

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Q: DO NOT include spaces in between characters. TYpe your answers in the following order and format: a=...

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 10x² an...

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Q: Evaluate f'(-2) if f(x) = x* – 5+ x-2 + 4x-4.

A: The detailed solution is given below Thank you 

Q: Given the vector function. Calculates the principal normal vector N(t) when t=6.9

A: Question- Given the vector function. Calculates the principal normal vector N(t) when t=6.9 ?      

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above th...

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Q: If we convert the point (p, 0, 6) = (6,7/6, 5T/6) from spherical to cartesian coordinates, we obtain

A: