Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

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

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Q: A balloon is rising vertically over a point A on the ground at the rate of 15 feet per second. A…

A: Let's draw the diagram first Given: dhdt = 15 ft/sec We have to find the value of dydt when h=40

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A: The given graph is distance against time ,  where distance is marked on y-axis and time marked in…

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A: We will check weather at x=2 and x=3 function have opposite sign. If sign is not opposite than there…

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Q: Find the average value of f(x)= 4x - 5 from 1 to 3. ... The average value of f(x) = 4x - 5 from 1 to…

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Q: Evaluate and simplify: 4sin(4)- csc(-) 2 A 1-2/7 B 1+2/7 -1-2/7 D -1+2/7

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Q: y = In (csc 2)

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Q: 15. Evaluate L s-3 A) 2e e" +t- 61 +t-61° B) 2e " +1-6t -1– 61 C) 2e" +t-3t² D) 2e" +1-3t

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Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

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Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…

Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. P…

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Q: 3. If g(x) = -dt, find g'(2). %3D

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Q: Find both first partial derivatives. z = Gy?V az az ay

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: 5. [sin-' x dx Ans. x sin'x - V1-x² +

A: We will use integral by parts to evaluate integration of arc sinx

Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: Evaluate the function at the given value of x. Round your result to three decimal places. Function…

A: Solve the given

Q: Use the properties of the derivative and the given vectors to find the following. = ti+ 8 sin(t)j +…

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Q: 6. Vectors i and v are positioned at 115° to each other such that lü| = 15 and l0| = 7. Determine…

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Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

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Q: n² < 2" for n = 4,5, 6, ... (Hint: 2n + 1 < 2" for n = 3,4, 5, ...)

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Q: Solve for x. log x = - 4 0.0001 -0.0001 1.386 -4

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Q: y = 9 - t

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Q: Regarding on the letter c, why is it equated to negative gamma?

A: c) The direction ratio of D→-C→ is -2, 5, -5 from part a. D→-C→ is normal to the required plane.…

Q: Fill In The Blank Refer to the given below. Find the indefinite integral. Simplify your final…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: Given x=et cost  , y=et sint , z=7 et

Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: 2 x – 4 dx .2 1

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Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

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Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

Q: Use the Newton-Raphson technique to find the value of a root of the equation e = sin 4x. An…

A: Given:

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: (b) Which of the following integrals is equal to –2+ ln 2? (a) 4 dx 4 (b) dx x² (c) / 4x dx x2 4 dx…

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

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Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 6 cos(t)i +6 sin(t)j+…

A: As we know that; The expression for the curvature; κ=r't×r''tr't3 And The expression for the radius…

Q: Find the second derivative (y") of the given function: 6. 2-e

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Q: Given the expression below, y = ecos arc sec(ln(r |- determine y.

A: The derivative is given below

Q: Find the arc length of the graph of r(t) eV2li +e¬V2lj+2tk, 0<t< v2 ln 9 NOTE: Enter the exact…

A: Given problem:-

Q: xe' – ye* = In(xy). Find dy/dx

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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: Find the root of x4-x-10 = 0 approximately upto 5 iterations using Bisection Method. Let a = 1.5 and…

A: The root of x4-x-10=0 between a=1.5 and b=2

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = 3xy and above…

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