Find the exact value of each of the following using a suitable power-reducing formula cos²(67.5 14√2 22 O √√2 2-√2 2+12

Q: Let f(x, y) = x³ + y³ + 3x²y + xy + y². Find fæ, fy, fax, fry, fyy.

A: The given function is,

Q: Differentiate the following function: g'(x) = g(x) = 4x³ + 8x5 + 1

A: Differentiate the following function

Q: A Norman window is made up of a semi-circle and a rectangle. The total perimeter of the window is 16…

A: A Norman window is made up of a semi-circle and a rectangle. The total perimeter of the window is 16…

Q: Find a polar equation for the curve represented by the given Cartesian equat x² = Sy O a.r=8 cos sin…

A: given

Q: Find the average value fave of the function f on the given interval. 10x - x², [0, 5] f(x) =

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Q: Consider the position function for free-falling objects. s(t) = -16t² + vt + so A ball is thrown…

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Q: Suppose the second derivative of f is given by f'(x) = 15x4(x + 7)5(x² + 36). Determine the…

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Q: Given f(2)= 35, f'(2) = 8, and f"(x) < 0 for x ≥ 2, which one of the following statements about f(6)…

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Q: Find a vector a with representation given by the directed line segme A(0, 4, 4), B(4, 4, -2) Draw AB…

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Q: Below is the graph of the DERIVATIVE of f --- that is, the curve y = f'(x) is pictured below. y =…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Given f(2)=40, f'(2) = 3, and f"(x) = 0 for x ≥ 2, which one of the following statements about f(10)…

A:

Q: A rock is thrown off of a 100 foot cliff with an upward velocity of 50 m/s. As a result its height…

A: A rock is thrown off of a  foot cliff with an upward velocity of . As a result its height after…

Q: dy Find by implicit differentiation, where 3x7 + 4x²y7+y³ = 4. dx dy dx

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Q: A silver dollar is dropped from the top of a building that is 1322 feet tall. Use the position…

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Q: Let f(x) = -5x(x − 1). Then ƒ'(−3) =

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Q: Determine the corresponding ordered pair of the point on the unit circle for the following angle:…

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Q: Use the derivative f'(x) = x²(x-3)(x + 3) to determine the local maxima and minima of f and the…

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Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

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Q: -15 Use the graph below of k(z) to evaluate the following limits: (a) lim k(x) = (b)lim k(x) =…

A: Note: As you posted multiple subparts I need to solve only first three subparts.

Q: Please find equations for the lines tangent to the graph of f at the point where x = a.  f(x) = 2x3…

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Q: 12 Let. f(x) = ¹2. Please find f'(x), ƒ'(3), and the equation of the line tangent to f where x = 3.…

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Q: Consider the planes given by the equations (a) Find a vector parallel to the line of intersection of…

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Q: Use a linearization, or differentials, to approximate the value of $7.95.

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Q: find fz (2²+1) da can not be done 0 x¹ + x² + c © x³ + x +1 Onone of these answers

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Q: Find the reference angle, 8, if 8 = 1395°.

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Q: Given ƒ(7) = 3 and f'(7) = 4 find the value of h' (7) based on the function below. h(x) = (f(x))²

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Q: Consider the function f(x) = 3x + 5 X +3. Enter the number of critical points/numbers of f(x).…

A: Given;

Q: 4. a) For 0≤x≤ 1, show that < x² √1+x < x² b) Use the estimate in a) and integrate it to prove that…

A: We have to prove given inequalities.

Q: EXAMPLE 2 Find the area of the region that lies inside the circle r = outside the cardioid r = 1 +…

A: Here we have to find the area of the region that lies inside the circle and outside the cardioid.

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: The region of integration;:

Q: To convert an angle in radian measure to degree measure, multiply by a factor of 180 O True False

A: Given,

Q: Find the volume of the region between the planes x + y + 2z = 3 and 4x + 4y + z = 12 in the first…

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Q: d dx d du d dz d [12 cos ¹2x] dy d dq [4 sec ¹3u] [10 tan-¹2z] [6 csc-¹4y] [9 cot-¹39]

A:

Q: Evaluate e 1 5x + 4 X dx

A: let

Q: The value of tan 8 of the right triangle shown below is 3 26 26 8 True False

A: Given

Q: Find the volume of the region bounded by the coordinate planes, the plane x + y = 6, and the…

A: x + y = 6 y2 + 25z2 = 36

Q: The following statement is a cofunction identity: sin(e) = cos cos (-e) O True O False

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Q: 2. (§5.5, 8.5) Evaluate the following integral: S Hint: try u-substitution first. 8 cos x sin³ x 4…

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Q: Find the absolute maximum and absolute minimum values of the function 4x 6x + 2 f(x) =

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Q: 2 Find the average distance from a point P(x,y) in the disk x² + y² ≤81 to the origi The average…

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Q: a. The usual way to evaluate the improper integral 1 = e 00 ²-[[eta][[eta]-[[- ´e¯v²³ dy = S S e¯…

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Q: A person stands on top of a 300 ft building and spots a person on the ground below. The angle of…

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Q: 3. a. A firm produces two different kinds A and B of a commodity. The daily cost of producing a…

A: As per company guidelines for multiple question posted we are supposed to solve only one question at…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 3…

A: First curve r= 3cos(theta)r= 1+ Cos(theta)

Q: The reciprocal function of sine is secant. O True False

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Q: (a) lim f(x) x→-∞ (b) lim f(x) x→-2 (c) lim f(x) x→2- (d) lim f(x) x→2+

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Q: Find the magnitude of a vector, v, whose initial point is (-5, 8) and terminal point is (2, 3).…

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Q: Determine the x-coordinates of the relative extrema of the function g(x) = Enter each answer as a…

A: The given function is,

Q: sin x To verify the identity = (secx-tanx)², a possible strategy would be to start on the left side…

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Q: Evaluate Limit = Use "infinity" for "oo" and "-infinity" for "-". lim 8118 3x4 - 3x² 5x6 +8

A: