Part 3. Provide solution in finding the derivatives of the given function 1. y= 4x5-2x + 3x- 10 2. y = V4x3 - 16 3. y=lnx2 4. y=

Q: +t, 2t +t, 6t} O sis a basis of P O sis not a basis of P3.

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: Let a = ci + jand b = 3i + 4j. Find c so that the angle between a and bis Round your answers to four…

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Q: 17 + sin w sin(1+ cos w)) dw 7-2w

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: To use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: 13 dt 9+6t 4 (9+6t)5

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 4 V3 and whose components have…

A: Given:     Let v=x,y,z be a vector in R3 with length v=43 This is x2+y2+z2=43            x2+y2+z2=48…

Q: 7 If D is the region enclosed by y =-, x = 7, and y = 7x. Then %3D ly dA = 1386. D Select one: O…

A: Solution is given below

Q: (30.4) Apply the ratio or root test and state whether the series is convergent (2n)! n=1 or…

A: Given:     series ∑n=1∞12n!     Split the series:     =∑n=0∞12n!+∑n=00-12n! Since the bounds are…

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Here, note that any plane through the point P(14,-12,7) is of the form:…

Q: Find the area bounded by these curves. (All choices are in sq. units) y1 =+4 Y2 = r-2x

A: This question is related to application of definite integration, we will solve it using given…

Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

Q: Find the vector component of v = 2i – j+ 3k along b = i+ 4j + 8k and the vector component of v…

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Q: Prove the identity sin x cos²x+ sin?x algebraically and CSC X determine the non-permissible values…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A: To find the unit vectors that satisfies the given conditions.

Q: Find the vector component of v = 2i – j + 3k along b = i + 4j + 8k and the vector component of v…

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Q: atical expression or equation. x is nine more than five times the one more than three times the nur

A: We have to convert in mathematical form from the given information

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

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Q: The are of a rectangle is 100 cm2 and one of its sides is x cm. Find the minimum perimeter possible.

A: Let us consider a rectangle with length l unit, breadth b unit Then area of this rectangle= lb…

Q: The following Riemann sum gives the Right-Endpoint approximation of the area under the curve of some…

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Q: Consider the mass-spring system for mass 0.5 kg, spring constant 4.8 N/m, and an oscillating force…

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Q: S sin x In(cos x) dx

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Q: Find the area of the parallelogram that has u = 2i – 3j + 2k and v = 2j + k as adjacent sides. NOTE:…

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Q: Identify and sketch the graph of the following equations in R'. (a) x² + 2y2 + 22 – 8x + 12y – 2z +…

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Q: 1+ tan² x y = y = 2 sec x + tan x sec x

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Q: Evaluate the following integral using trigonometric substitution. хах Vx2– x – 1 а.

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Q: 3. Find the area of the region in the first quadrant that is enclosed by the coordinate axes and…

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Q: EVALUATION Directions: Find the derivative of the following functions. Choose the best answer from…

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Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: Find the area bounded by these curves. (All choices are in sq. units) y = x? y = 4x – x2

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Q: 7458 B2 Follow the solution format on the picture.

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: Find the vector component of v = (4, – 1, 7) along b = (2, 6, –9) and the vector component of v…

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Q: Find the directional derivative of f at P in the direction of a. f(x, y, 2) = xy + 2²; P(2,-5, –1);…

A: Given query is to find the direction derivative. BB

Q: A horizontal aluminum rod 4.9 cm in diameter projects 4.4 cm from a wall. A 970 kg object is…

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Q: Solve the differential equation with appropriate method. Finalize answer equated to ky^n. dy/dx + y…

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Q: A water pipe having a 2.88 cm inside diameter carries water into the basement of a house at a speed…

A: Here, the given radius of the first end is r1=2.882=1.44 cm Now, the speed at the first end is…

Q: Evaluate * | (0² + 1) cos 0 d0. e2sine + 20cose – sine + c 02sine – 20cos0 – sine + c Option 1…

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Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

Q: Find the directional derivative of f(x, y, z) = at P(4,5, –3) x + z _n the direction from P to Q(3,…

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Find all the complex roots. Write the answer in exponential form.   The complex fourth roots of…

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Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 6, 11), and (1,0,-1).…

A: Given

Q: 4. The function g(t) = (8t)' – cosh² t + sinh t satisfies g'(c) = 0 for which value of c? (a) c= 0…

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Q: Find the area bounded by these curves. (All choices are in sq. units) y = x 4x +y = 12

A: Here, the is a line passing through the origin. And,  4x+y2=12⇒4x=-y2+12⇒x=-14(y-0)2+3 which is a…

Q: 1 (5* )csch- if y= (e oshS ) In Vx² +1 2 a) Find dx dy x+1 x>0. 2 x++1

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