Find the (2x + 1)³ dx A. (2x + 1)2 +c (2x + 1)3 + c 8 С. (2x + 1)4 + c D. (2x + 1)* + c 4 B.

Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

A:

Q: _1. (2x – 3) dx А. —2 - _2. L (x³ + 2x) dx В. 0 _3. (x² – 2) dx С. 3 1 -

A: 1) ∫02(2x-3)dx2) ∫-11(x3+2x)dx3) ∫03(x2-2)dx

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find the volume of the given solid using triple integral.

Q: Find the area of the region bounded by the curves y = 1/x , y = x and y = 4x in the first quadrant.…

A:

Q: What is the period and domain of the basic cotangent function y= cot(x)? TT, {x €R|x=kT, kEZ} B 2 C)…

A: We can solve this as follows:

Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

A:

Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

A:

Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: Sketch a single graph of a function f(x) which satisfies all of the following the limits and values.…

A:

Q: 14. Evaluate L{e" cos(30)}. s-4 A) s - 8s +25 B) s - 8s + 25 4 C) s - 8s + 25 s+4 D) s - 8s +25

A: As we know that the Laplace identity; 1). If Lft=Fs then Leatft=Fs-a  2). Lcosat=ss2+a2   Given:…

Q: Evaluate the limit: r(t + h) – r(t) lim h >0 for r(t) = (t°, sint, 1) h r'(t) = (

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Q: Find the general solution of the differential equation. 4dy + ydx = x²dy

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: 2 _9 ii)lim- t-3 t2+4

A: Given query is to find the limit of the expression.

Q: Write down the first four terms of the sequence given by x, = 3" + 2", starting from n= 0. X1 = X2 =…

A:

Q: What I Have Learned Let us now measure what you have learned in this module. Choose the letter of…

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Q: Assume that f(x)dx = 3 and g(x)dx = -2, find the following: 1. Sf(x) + g(x)]dx = 2. S12f(x) – g(x)]…

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Q: If y=f(x) = - 3cos+) + 4 then what is the value of / 2 A) 7

A:

Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

A:

Q: im Y cosx t Zx メナロ0 7x¢ し

A: Given query is to find the limit of the expression.

Q: d d Calculate r1(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Find the derivative of the following function by applying the appropriate derivative rules. f(x) =…

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Q: sec" /x dx 17. 2 5n Ans. 6

A:

Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e*, -6), g(t) = 5t + 6 %3| 을r(g(t)) = 《

A: Use chain rule

Q: P1. 18. Which of the following is true? Select one: O a. AxB is the same as BxA O b. If vector A is…

A: Vector

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

A:

Q: cos x e) f(x)= e* х

A: Topic = Derivative

Q: Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

A:

Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

A:

Q: The study of integrals in calculus is motivated by the problem of calculatin (a) the slope of a…

A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: 1

A:

Q: Let f (x, y) = e(8x-9y). Find the equation for the tangent plane to the graph of f at the point…

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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Q: Find the limit. lim (t i – 3 j+ t?² k) t-2 lim (t i- 3 j+1? k) = j + i i+ i i k

A:

Q: Solve the equation for x and y x+v=300 5x+8y=2100

A: Given query is to find the solution of the system of equations

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A:

Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

Q: A small resort is situated on an island that lies exactly 4 miles from PP, the nearest point to the…

A:

Q: For each sign chart for f. Carefully sketch the graph of both functions f and f. Upload your work as…

A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

A:

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. 2(3*)…

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Q: stimate using the trapezoid rule and Simpson's rule for et dx;n3D8 -2x+5

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Q: Evaluate the double integral over the rectangular region { 2(* sin(1) – y sin(z) dA; R= {(x,v) : 0 <…

A:

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.