E A4 sin (e-² + ln z) + C 4 sin (-e-²) + C B O A § 4 (½ − e¯²) cos (e¯² + Inz) dz B E None of the Above C sin (e-² + In z) + C sin (-e-²) + C D

Q: area bounded by a = √y, x = 0, and y = 3 with the axis of revolution at y-axis using horizontal…

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Q: 5. The angle between the tangent line and the normal line is (a) 180° (b) 90° (c) 45° 6. If x= 3t-2…

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Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

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Q: For the limit, lim (x,y)-(0,0) if we approach along x-axis, we will get 0. Select one: True sin(x² -…

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: Evaluate fz² In z dz using integration by parts Oz² Inz-+c Oz-+c Onz-+c Oz²lnz-/+c 12 2₁

A: A detailed solution is given below

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A: Here we have to find the slope of the tangent line.

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Q: In³ w 3 w√In²w-4 mp

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Q: 2n Consider the series ₁ (-1)" (1 + 1)². Which of the following statements is true? n=1 The series…

A: A series ∑n=1∞ an is said to Converge Absolutely if the series ∑n=1∞ an converge and Conditionally…

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A: We have to find the x1, x2 , x3.

Q: 5. (x² + y² + 1)dx - 2xydy = 0

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Q: QB3) Verify fxy-fyx for the function f (x, y) = 4x (Iny) + 4y (Inx) + (²²4 2²

A: We have to prove fxy=fyx for the given function.

Q: If z = √√√xy, dz and x = t², y = 1² then =? dt Select one: O √xy(21) O √xy(21²) 0 2t O None of them…

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Q: Given that the graph of f(x) passes through the point (5,10)( and that the slope of its tangent line…

A: Given , The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at…

Q: 3. (x² + y²)dx - 2xydy = 0 [Answer: x²-y² = cx]

A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

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Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: Question 22 A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of…

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Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

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Q: (c) lim ln(csch ¹x) #+++∞

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Q: The following limit Select one: O O equals 16 3 equals 0. None of them O does not exist. O equals 3…

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Q: 14. Show that the demand function D(p) =alp', where a and b are positive real numbers, has a…

A: Solution is given below:

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Q: Find the determinate by expanding about the 1st row. 1 3-1 223 1-1 0

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Q: If f(x, y) = Select one: O None of them In (x² - y) then the domain D of the function f is given by…

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Q: Question 1 described by the vector function r(t) = (4t² ln t, t-4 29 -2e-³t). a) Find the integral…

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Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: See this solution in below

Q: The figure has a tangent line drawn at a labeled point. c(t) thousand chips 8 6 4 2 (1.95, 7.07 0.5…

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Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: topic- application of derivatives

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Q: Evaluate S ○ In O Divergent ○ In 11 O 6 In 11 6 dz 2²-25 16

A: Given problem :- ∫6∞6x2-25dx

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Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

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Q: If f(x, y) = √6xy - 4x + 30y then fa = Select one: O True O False -4√6xy+3y √6xy

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Q: lower sum upper sum Function f(x) = 9 - 2x s(n) = S(n) = Interval [1, 2]

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Q: (4x² - 9)72 99

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Q: f(x, y) = Find fx, fxy, and fxyx. 7 8x+5 + 8x³ e-8y

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Q: Let f(x) = 2x - 13. Determine f-1¹(x).

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Q: If then fxx = Select one: True False 2(y² + y) (y - x)³ f(x, y) = x + y² y-x

A: According to question,Given Function,fx, x = x + y2 y-x

Q: Let z =ellxy-56y and x =5616 + 6 and y =sin(s + 56). Use the дz дz Chain rule to find and dt - дл

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Q: If p = (7, 2), then find -2p.

A: If p=7, 2, then to find -2p.

Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

Q: x² 2 =dx 2 √4+x²

A: solution:-∫x24+x2dx=4∫x2441+x24dx=2∫x221+x22dxwe know thatcosh2t-sinh2t=1cosh2t=1+sinh2tusint…