6. g(x) = sec (3x²)

Q: 1 cos(4(1.001)-4) 2((1.001)-1)

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Q: Q4/An armed paratrooper weighing 320 lbs. jumped with initial velocity from an airplane at an…

A: Solution

Q: a. Find the differential equation by eliminating the arbitrary constants of the family of curves  ?…

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Q: Let f(x) = (1 + 7x2²)(x - x²).

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Q: Given r(t) = 5t8i - 9 sin (t)j + e³tk and s(t) = −4ti +8tj+4tk, find [2t² r(t) + 2t¹s(t)]. dt Sorry,…

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Q: 14 = √ √₁²-x² dx

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Q: A population of 580 bacteria is introduced into a culture and grows in number according to the…

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Q: h = [(xcos.x)² dx

A: To evaluate the integral without using substitute.

Q: Let f(x)=5x+7 Let g(x)=ln(x)−3 Find the following: (1.) g(f(x))= (2.) f(g(x))= (3.) f(f(x))=

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Q: 2. y' = 2y4+x4

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Q: Q2: Construct the difference table from the following data. x y 0 1 1 4 2 21 and then find y" (3.2),…

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Q: Question Find the antiderivative of r' (t) = (est, e-7t₁ -&) that satisfies the initial condition…

A: Given: r'(t)=e5t, e-7t, -6t9

Q: 2) 2xy + y² - 2x = 0 dy dx Ax

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Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows:

Q: Given the following graph, determine the limit of the function as x approaches -2 does not exist 16…

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Q: (a) Find the volume of the solid bound by the parallelopiped formed by the vectors a = (−2, 0, 5), b…

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Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1−x)y''+ (2x²− 1) y'+k (2x − 1) y=0…

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Q: 2. To the right, you are given the graph of the function 2-2 x-1 f(x) = 22 x1 x 1 (a) Use the graph…

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Q: Given the table below: -4 -2 -1 1 9 7 5 g(x) 10 9 3 4 I Evaluate ()-[ (4) 9 -3 Check Answer 0 2 6 2…

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Q: Given f(x) = 6/x find f’(x) using the limit definition of the derivative. f’(x)= Please explain step…

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Q: Evaluate the general solution of y""=e4x + sinx

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Q: Evaluate the general solution of y""=e4x + sinx

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Q: What function is the general solution of the differential equation y" +10y +25y=0? = (Ax+B)e-5x y=…

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Q: f(x) = wo values of b for which f is a continuous function at -1. with the greater absolute value is…

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Q: aken in years. Determine the time T taken, to the nearest year, fo riple. OT 21 years T≈ 15 years

A: Topic:- application of calculus

Q: A vector field is defined as: v(x) = (xx)x= xixmme. Which of the following tensor fields represents…

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Q: . Compute the derivative (r₁(t) · r₂(t)) if r₁(t) = (tº,t7, t8) 1₂(t) = (e¹0¹, e²¹, e³¹) (Use…

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Q: 1. For the given functions, state the range and find (f-¹)(a) using th ate formula for the…

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Q: Eliminate the arbitrary constants Y = C₁ e²x + C₂ C³x са

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Q: What is the magnitude of the cross product between (3, 0, -4) and (2, 0, 1)? 5 11 √2 2

A: SOLUTION-

Q: Suppose that f(5) = 1, f '(5) = 4, g(5) = -8, and g'(5) = 2. Find the following values. (a) (fg)'(5)…

A: For a pair of function f,g we have the following.(i) fg'=f'g+gf'(ii) fg'=gf'-g'fg2

Q: Evaluate lim 24-2+ 1 -X 1 X

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Q: What is the rule of the inverse function of f(x) = (5/x) + 3

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Q: 3/5=-3n

A: We have to find the value of n from the given condition

Q: A visitor is staying in a tent that is 7 miles west of the closest point on a shoreline to an…

A: We have to minimize time taken to reach at the island from camp.

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: 16 = dx / x7 3/5+4x⁹

A: This question has been solved without using trigonometric substitution

Q: Eliminate the arbitrary constant Y = cx+c²+1

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Q: 8. Evaluate the definite integral without using the calculator. √3 1 (a) [√3/2 √ 1 √1-x² dx (b)…

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Q: 2. g(x) = COSX

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 2x y at the point (2,9).

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Q: 4. Find the value of the constant b for which f is continuous at a = - -1 and determine f(-1). 5 x <…

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Q: In a certain sci-fi apocalyptic movie set in the year 3020, the narrator said the maximum acceptable…

A: Given: In year 3020, Rate of decay of atoms of Uue is proportional to the amount present. After 10…

Q: lim 2"-1 = x-0 A B C D 0 In 2 1 1 In 2

A: limx→0ax-1x=lna

Q: By determining f'(x) = lim h→0 f(x) = 8x² f(x+h)-f(x) h 1 find f'(5) for the given function.

A: As per the rules we can answer only the first question and other can be reposted,

Q: Solve for the particular solution of the differential equation below when s=2 and 0=π/4 tanede +…

A: I am attaching image so that you understand each and every step.

Q: Find  f(a),   f(a + h),  and the difference quotient  f(a + h) − f(a) h,  where  h ≠ 0. f(x) = 9…

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Q: Evaluate the integrals (5) (6) (7) f cos2x sin²x dx tan’xsec’xdo f tan³x sec5x dx

A: Here we have to integrate the given function

Q: Dis the resultant of which two vectors? Vector D 4 B D

A: Given,

Q: If A any non-zero vector, a unit vector in the same direction of A would be: A AA 0-AA - A

A: