dx 17. S√4e-2x-25

Q: 8. y = x ¹ Arctan 4(x4)

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Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0),where sin x f(x, y) = x (x, y)…

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Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: The position of an object moving along a line is given by the function s(t)= - 8t +72t. Find the…

A:

Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

A:

Q: Find the length of the arc of a circle of diameter 1010 meters subtended by a central angle of π4π4…

A: Solution ) diameter - 1010 m , angle = π/4 Radius =  1010/2           = 505 m length of arc of…

Q: Using Fundamental Theorem of Calculus (FTC). Compute the following

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Q: a. The object's velocity after 5 seconds is (Round to the nearest tenth as needed.) m/sec.

A: We have to find the velocity after 5 sec

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: 2. 5x - 2 (x + 3)² S dx.

A:

Q: y = (4 + ³√/x)³ 3

A: Inverse function

Q: Use the one-to-one property of logarithms to find an exact solution for   ln(2)+ln(2x2−6)=ln(69)…

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Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: The degree of DE: (y")^2 +3y(y')+y^3 (y')^5 = 5x 02 01 05 0 3

A: Recall:  The degree of D.E. is the highest power of the highest order derivative in a D.E.

Q: y = ln √4x² (Hint: Apply first a property of LOG.)

A: Let's find first derivative.

Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

A:

Q: B. Find the general solution of the following 2nd order differential equation: y*+2y+2y=0

A: The given second order homogeneous differential equation is: y''+2y'+2y=0 Therefore, the auxiliary…

Q: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: 5 8. fcscz x cot3 x dx

A:

Q: Suppose a population of fruit flies changes at a rate of g(t) = -3e0.01, in flies per day. If the…

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Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Find the determinant of A) -10 B) 0 C) 14 (D) 10 1 3 [42]

A: We can find the determinant as below

Q: ind A or each of the following intervals, tell whether f(x) is increasing or decreasing. -∞o, A):…

A: Topic:- calculus

Q: Find a potential function f for the field F = 4y + 5z ( i + 4x j + 5x k). A general expression for…

A: Solve as general

Q: (D³ + 2D² - 5D - 6)y=0; y = 0, Dy=0, D²y = 1, when x = 0.

A:

Q: Determine the magnitude of the vector sum V-V₁ + V₂ and the angle 8, which V makes with the positive…

A: We have to find the vector and angle.

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

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Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

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Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

Q: ow that the differential form in the integral below is exact. Then evaluate the integral. 5,1) 20x…

A: We have to examine that the given differential form of intregal is exact or not .after that we have…

Q: Look for the volume of the solid produced by rotating the region enclosed by y = sin x, x = 0, y =1…

A:

Q: let G={h: [0,1] approaches to R: h has an infinite number of derivatives). then G is a group under…

A: We need to find f inverse of (g) and show it is a coset of ker(f).

Q: dx 15. S (x²+36) ³/2

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Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: (b) In +8 x² 2 - 36

A: We have doing solution useing logarithm laws

Q: Problem x√x+1 dr

A:

Q: 5x +34 if x - 6 2 if x = -6 Select all statements below that you agree with. Note: You may be…

A: We

Q: 1. Jổ xdx xdx ull ch 2. √²2² (x²-x)dx 3. f2, xdx

A: We have to solve as per guidelines Solving by fundamental theorem of calculus

Q: Fill in the blanks in the following: 1. Ifa (3,-2, 6) and b=(4,-1,-6) the axb:

A:

Q: B. Graph each equation. 3. 3x²2y² - 12x + 12y = 12 4. x² + 2y² + 2x - 8y = -5

A: Graph of : 3x2 - 2y2 - 12x + 12y = 12

Q: (d) Given r(t) = (ln(t+1), t cos 2t, 2¹). (i) Find r'(t). (ii) Find parametric equations for the…

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Q: iv) in complex number z³. (z)² = |z|².z

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Q: Derive the following function 1 1. v = x²√x + √²²³√x 2. g(r) = (r²2r)er

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Q: A tight headed northeast from P-City to Q-on was sent 10 degrees off course by high winds. The plane…

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Q: 4. f²₁(x² x)dx 5. (4- x²) dx

A: topic- definite integral

Q: Find the Differential equation Ⓒ (y + x²) dx = x dy

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 6. f cos¹ 2 xdx

A: Given,  ∫ cos7 2xdx

Q: 8 Find the area bounded by y y = 2x, y=0 and x = 3. X Using vertical element, what is the integral…

A: