хах 3. S cos (2-3x2)

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: Use the formula for the binomial series: m(m–1) ,2 + (1 + x)" = 1+ mx + 2! m(m–1)..-(m-k+1), k! %3D ...

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Q: The solution of the given equation (1+x²) y' + 2xy = 4x² is: O y=[(4x^3)/(3(1+x^2))]+C(1+x^2) O y=[(...

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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: Tim Hortons estimates it will have a continuous income flow of  f (t)  =  4311 dollars per year from...

A: Given income flow f(t)=4411 dollar.

Q: Evaluate the definite integral 7 (182 – 2x + 9) dæ 3

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Q: dy Find using implicit differentiation, for the equation a + = 11 is. da

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Q: 11 Find the area of the region bounded by y = x² + 2x – 1, y = + x x = -3, x = 1. 2

A: Area between curves

Q: The coefficient of sin ( 2x) in the antiderivative of

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Q: Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile i...

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Q: Evaluate: ,(3y6 + 8y* – 9y²)dy 2

A: Given:    ∫-22 3y6+8y4-9y2dy

Q: Write an equivalent double integral with the order of integration reversed. dy dx dx dy dx dy ©SS ax...

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Q: If g is continuous at a and f (x)=(x² -a' )8(x). fir find f'(a). Hint: Use f'(x1) = lim S(x)-f(x,) %...

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Q: Show your work to justify your answers. Write your solutions properly, neatly, and carefully. s) Fin...

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Q: Consider the parallelepiped with adjacent edges u = 9i + 7j + k v = i +j+ 6k w = i+ 9j + 4k Find the...

A: We can find the volume as below

Q: If f(x) = 8 cot 1x + 4, then find the value of f'(-3) is -8 10 8 10 3 10 4 10

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Q: A pharmaceutical company is testing a new drug. After a person takes A0 mg of the drug, the amount o...

A: Question- A pharmaceutical company is testing a new drug. After a person takes A0 mg of the drug, th...

Q: A potato is launched vertically upward with an initial velocity of 121 ft/s from a potato gun at the...

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Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v ortho...

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Q: = sec.x-/2 tan .x , find f' (=). %3D

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Q: Determine if the lines intersect, or are skew, or are parallel. L1: x = 4+ 2t, y = -5+ 4t, z =1+3t L...

A: We will find whether the lines intersect, or are skew ,or are parallel as following.

Q: (주) X X Evaluate: " sin' cos* () d 4

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Q: -1 2. cos

A: 2.cos-1-12

Q: 3 is convergent or 24n-2 Determine whether the series Ć diveryent. It itis convergent, find its Sumi...

A: Topic:- sequence and series

Q: If f(x) 3 cot lr+ 4, then find the value of f'(-1) is > 8 m IN O O

A: Solve the function

Q: Determine whether the series converges using the Ratio test. 00 7k k=1 The series

A: This question is based on Ratio test.

Q: dy/dx

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

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Q: 2t dt (use trigonometric substituion) V9 – 4t2 -

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Q: A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 t...

A: The given problem is solved below in detail.

Q: If f(x) = 3 cot ' + 4, then find the value of f'(-1) is.

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Q: Evaluate: S,(3y6 + 8y* – 9y?)dy 2

A: ∫-223y6+8y4-9y2dy

Q: The integral of t2ln t with respect to t is; A (3ln t-1)+C B ®(3in t-1) +C none of the given choices...

A: Given: The integral of t2lnt with respect to t

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following s...

Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

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Q: From the following results, determine whether the function 2x +9, r 9 f(x) = 6. is continuous at = ...

A: Solve for the continuity for the function

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: Let a = ci + j and b = 2i + 10j. Find c so that a and b are orthogonal. c =

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Q: If g is continuous at a and f(x)=(x² -a )g(x)., find f'(a). S(x)-f(x,) Hint: Use f'(x1) = lim x-x1 %...

A: Given query to find the derivative at x = a.

Q: Consider the points A(3,-3, 3), B(4, -5,0), C(-3,-4,0), and D(6, 2, -6). (a) Find the volume of the ...

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Q: At which point/s (value/s of x) is the function continuous but not differentiable? -4 2 4 6 8 10 42 ...

A: Differentiable

Q: If f(a) = 7cot- * +2, then find the value of f(-4) is, 17

A: Given query is to find the derivative and indicated value of x.

Q: Find the centroid (, j) of the region bounded by: . y = 3x + 8x, y = 0, x = 0, and x = 6 %3D y =

A: The given problem is solved below in detail.

Q: Using an appropriate substitution, cos x-sin x the integral dx equals: 2 cos x+sin x -1 none of them

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Q: A potato is launched vertically upward with an initial velocity of 101 ft/s from a potato gun at the...

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Q: fcac) fCre)ニ2x+5

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

A: This question can be solved by applying the formula of linear approximation.

Q: Rewrite the following integral using substitution: " s in3xdx

A: We can rewrite the integral using substitution as below.

Q: • Use the trapezoidal rule with n = 8 to approximate %3D cos(x) dx Keep at least 2 decimal places ac...

A: USE Trapezoidal rule with n=8 

Q: 8. x- 3x + 2 = -8 9. 7z -3 = 3 +6z 10.-8 -n = n- 4n 11.4n – 40 = 7(-2n + 2)

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