If find f'(x). Answer: f(x) = 4 sin x 3 + cos x

Q: Question 18 Find y' implicitly if 5y²2 + In(x + y) = x² 2x² + 2xy 10xy + 10y² + 1 y'= y'= y'= y'=…

A: To find y'

Q: 1) Given vectors à = (1, 2, 3), b = (-3, 1, -2), and c = (1, -2,-4), find ANY FOUR of the following:…

A: Scalar multiplication of a vector is obtained by multiplying the scalar by every component of the…

Q: In Problems 63–68, find f'(x) and find the value(s) of x where the tangent line is horizontal.

A: We can solve this as follows:

Q: (a) Evaluate the integral 40 -dx. x²+4 Your answer should be in the form k, where k is an integer.…

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Q: Use the Product Rule to compute the derivative: ((t² + 1)(t + 9))|t=6=

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Q: Let f(x) = (3x − 4) (x² – 5). Find all the values of x for which f'(x) = 0. X Present your answer as…

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Q: xp_G + +*) (; - x),J (

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Q: Let f and g be functions that satisfy f'(2) = -8 and g'(2) = 13. Find h' (2) for each function /…

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Q: A 64 gallon tank is filled with pure water. Water which has a concentration of 2g of salt per gallon…

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Q: Question 11 Find the proportions of the circular cylinder of largest volume that can be inscribed in…

A: The volume of circular cylinder = πr^(2)h           When the volume is maximum    Height h = radius…

Q: Evaluate lim (x,y) →(0,0) x³ +35x² + 7y²2 5x² + y² 11

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Q: Find the equation of the tangent line to the curve y = a√ at the point (16, 64).

A: To find the equation of tangent line to the given curve.

Q: 2 Mr. Gonzalez is designing a planter box shaped like a rectangular prism. The height of the box is…

A: Volume of rectangular prism(V) =l×w×hwhereV=volumel=lengthw=widthh=height   Volume of rectangular…

Q: how did you integrate cos2x to sin2x/2?

A: how did you integrate cos2x to sin2x/2?

Q: For winning first prize in an essay contest, you are offered a choice of prizes: A. a single…

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Q: the for the dia and n 8.3 101 the he ight-chcular cyinder is puted using the values a Use the Linear…

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Q: A local printer produces Course Packs. Total cost as a function of number of Course Packs produced…

A: Topic - Cost function Fixed cost is the cost when there is no production.

Q: Find a formula for the exponential function partially defined in the following table. Round any…

A: An exponential function is of the form f(x)=a(b)x wherea is called as the initial valueb is known as…

Q: The equation of motion is given for a particle by s(t) = 2t³ − 7t² + 4t + 10 where s is in meters,…

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Q: f(x)= (4x+1)x³ ; x = 1

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Q: 18. Find the extreme values of f(x) = 2x³ - 9x² + 12x on [0, 3] and [0, 2].

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Q: Using all three conditions of continuity, determine if the following functions are continuous at x =…

A: We need to check that the given function is continuous at the given point.

Q: Find the derivative of the function. f(x) = (x3 − 10x)(3x2 + 2x)

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Q: 10. Explain what the following definition means, either give an alternative mathematicall correct…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

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Q: Differentiate f(x) = = Answer: df dx 2 252+2

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Q: Find the x and y coordinates of all inflection points. 5 3 f(x)=2x +3 What is/are the inflection…

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Q: Question 28 ·S Evaluate dx 1+ sin x + cos x x − Intan¯¯+¹ 1+ C x Intan = +1+C 2 x x Intan 2 + 1/2…

A: Topic = Integration

Q: Calculate the derivative indicated. Answer: d²y dx² x=8 where y=2 +6x²

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Q: In Exercises 23-52, find the minimum and maximum values of the function on the given interval by…

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Q: Given the geometric sequence: 77 12 find a formula for the n-th term: ao 11, ai An a2 539 144'

A: Given a0 = 11 a1 = 7712a2 = 539144

Q: the Squeeze heorem to find each of the limits: i) lim(x - 2) sin 2)³ x 2 2

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Q: problem describes a debt to be amortized. (Round your answers to the nearest cent. A man buys a…

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Q: Use the binomial theorem to identify the coefficient of x² in the expansion: (4x + −3)³

A: The expression is given as  (4x+-3)3    The binomial expansion for the given by (4x+-3)3…

Q: Calculate the second and third derivatives. ले || = 9. y = 7x²¹ - 4x² + 7x

A: Calculate the second and third derivatives.…

Q: Find the perimeter of the triangle whose vertices are (-1,-2), (11,14), and (-1,9). Write the exact…

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Q: 4 Jxdx = 1

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Q: Find the angle, in radians, in the figure below if S = 12 and r = 8. S O 2 23 20120 07 8 r

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Q: 3. 4. If a function f is continuous at a, which of the following statements, if any, MUST be true?…

A: To find whether statement is true or false.

Q: Lone оех X 11+3x -1

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Q: Use the graph of f'(x) to discuss the graph of y = f(x). Organize your conclusions in a table and…

A: Solution given below

Q: a. Sketch and/or carefully describe the graphs of the following surfaces in 3 dimensions (R³): i. x…

A: Given: i.  x = y2 Sketch of the graph of surface:   The surface of the graph is parabolic cylinder.

Q: Find equations of the tangent lines to the curve y = x + 1 that are parallel to the linex - 2y = 4.…

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Q: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls…

A: Then volume of a solid obtained by rotating about the y axis the region under the curve fxfrom a to…

Q: Find du dy du du' dx dy dx y= u51 and u=2x³ +3x² || 1 and

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Q: 1 f(x)= (4x+1)x³ ; x=1

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Q: f(x) = 3 x° - 8 2 x + 5

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Q: 1. Let D = [1,2] × [1,3]. Evaluate [[ (x³y² + sin(√x)dA.

A: Here is the solution:

Q: Use the Product Rule to compute the derivative: d & ((t² + 1) (t + 9)) |t=-: dt -2= ←

A: Please see the below picture for detailed solution.

Q: Så ta de dx X ) n = 10

A: We have to find out the area of using the trapezoidal rule.