In considering normal and tangential components, the t axis is tangent to the curve at the point that coincides with the location of the particle and negative in the direction of decreasing s. O True O False

Q: 10.) volume of 480 ft'. The bottom will cost $5 per square foot to construct and the sides and top w...

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Q: Sy? sin y dy

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Q: 4. ху" + у' — хInx 3D 0

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Q: Find the antiderivative, G(t), of the function g(t) = (5n²t² – t4)V5n² – t².

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Q: Set up (do NOT evaluate) a rectangular double integral which gives the volume of the solid in the fi...

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Q: 17. A landscape gardener wants to build an 8000-square foot rectangular display garden along the sid...

A: Let the lenght of the garden is =x foot  Breadth is = y foot  Therefore, area = lb  8000= xy  Now we...

Q: Activity 1: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³...

A: We can solve subpart a,c& e as below.

Q: Evaluate the integral. 6 sin x dx -1 %3D NOTE: Enter the exact answer in expanded form.

A: To evaluate the given integral.

Q: Express the integral in terms of the variable u, but do not evaluate it. eS-4 dz; u = 5z – 4 NOTE: E...

A: ∫01 e5x-4dx  here change the variable x to u u = 5x -4 du/dx = 5 dx =du/5 limit is change from  if x...

Q: solve using Integration by Parts Trigonometric Integrals Trigonometric Substitutions

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Q: The base of a solid is the region in the first quadrant bounded by the graph of y = sin xand the x-a...

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Q: a) an en 3n

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Q: For each differential equation, indicate the order (as a number) and whether the equation is linear ...

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: x²dx Evaluate x2Vx2-4

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Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 8j as a...

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Q: Vx – x The lim x→1 In x

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Q: Solve the Lagrange's partial differential equation 2 z* p – xy(x² + yz)q = xz(x² + yz). 4

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Q: 6. Evaluate the following indefinite integral as an infinite series. sin x (a) (-1)". 2n+1 (b) (-1)"...

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Q: sinh(3x Solve for f(21) (x) given that f(x) =

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Q: pload answer sheets Find the Laplace transformation of H(t-4)e“-4)

A: Solution is given below:

Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x

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Q: x²dx Evaluate x2Vx2-4

A: Using standard formula for integrating the given indefinite integral

Q: x dx e

A: This question is based on integration by parts.

Q: х* + аx — 2bx — 2аb - х3 —2ax* — 2bx* dx х4 + ах3 — 2bха — 2аbx?

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Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: dy If y = x* then dx

A: This question can be solved by applying the concept of logarithmic differentiation.

Q: f(x,y)=x^2/y at (3,2)

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Q: 2x + y -4 44. -2y + 4z 0. 3x - 2z = -11

A: 44. Solution :2x+y=-4   .... 1-2y+4z=0 .... 23x-2z=-11   .... 3equation 2 1+24x+2y-2y+4z=-84x+4z=-8x...

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 4(x² – ...

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Q: Choose the statement that best describes this graph. Time O a) The stock price has decreased steadil...

A: . d) The stock price has fluctuated over the last week.

Q: (2 cos x–sin x )" dæ sin x

A: Given: I=∫2cosx-sinx2sinxdx   We know that; The trigonometric identities; 1). sin2x+cos2x=1 2). 1csc...

Q: Find the arc length function for the curve y = sin+(x) + V1- x² with starting point (0, 1). s(x) =

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Q: Evaluate (*(x-2) (х-1)3

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Q: xy² dy dx x2

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Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

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Q: cos x dx – sin z V1- sin x Determine

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Q: (y- 2xy +6x ) dx-(x – 2xy + 2) dy = 0

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Q: Find an angle 0 with 0° < 0 < 360° that has the same: Sine function value as 250° 0 = degrees Cosine...

A: Given query is to find indicated angle.

Q: Vx- 2 dx E+ 1)

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Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96, 1.02)...

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Q: 13 8 cos 37 + i sin 8 |10 + i sin 16 Cos 16

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Q: Find the derivative of the follo solutions. 1. What is (5x +3)4? dx 2. What is 4 (x2 – 3x)5? dx 3. W...

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Q: Consider 5 a8 +2 x2 +2 sin(x)–2 f(x) = %3D -28+5 x+5 Find the behaviour of f(x) as x → oo. • If lim ...

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Q: Find all critical values for the function f(x) = 10x – 30x + 5, and then list them (separated by com...

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Q: ( 2x + y -3z = 0 -2x + 2y + z = -7 3x - 4y-3z %3D %3D 7

A: We have to solve the system of linear equations.

Q: y = x2, y + 2x =8. ntify the volume generated by revolving amd y = 0, rotated about the y-axis.

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Q: dx = x[4 + 3xsin(ay)cos(ay)] dy

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