Calculus I Consider the following graph y=f(x)  Where dy/dx is zero?

Q: Determine whether the differential equation (4x² - 2xy + 5) dx + (7y² − x² + 4) dy = 0 is exact. If…

A: The given differential equation is;  (4x2-2xy+5)dx+(7y2-x2+4)dy=0.

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

A: As per our guidelines we are supposed to answer only first three subparts of the question. Kindly…

Q: Find the solution of the given initial value problem in explicit 1 y' = (1 — 11x)y², y(0) = ——— 6…

A: We can solve the given differential equation by using the variable separable method.

Q: Determine the total area bounded by the functions f(x)=-x2+2 and g(x)=x3-x2-x+2.

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Q: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field (the fourth…

A: A farmer has 400 yards of fencing and wishes to fence three sides of a rectangular field.

Q: Culator. A particle is moving with velocity v(t) = 1²- 9t+18 with distance, s measured in meters,…

A: The objective is to find total distance travelled.

Q: x-2x +x= 15; x (0) = 7, x (0) = -16

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Q: A particle is moving with velocity v(t) = t2-9t + 18 with distance, s measured in meters, left or…

A: The objective is to find instantaneous velocity and speed at time t=5sec.

Q: Find the general solution of the given differential equation, and use to determine how solutions…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Figure 1 shows a continuous piecewise function's graph. f(t) 4 3 2 1 1 2 3 4 Figure 1 a) Based on…

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Q: Consider the level surface defined by the equation x² + 2y²-32² - xyz = 8, find the following: a)…

A: Given problem:- Consider the level surface defined by the equation x2 + 2y2 - 3z2 - xyz = 8  Find:-…

Q: 7 22 +22=²-10 2x round to two decimal places

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Q: dy dx separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the…

A: To find whether given differential equations are which one of the following in the given options.

Q: x/8 sin 3r cos 5r dr

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Q: Tess tried to solve the differential equation = 2xy - 6x. This is her work: dy = 2xy - 6x dx dy Step…

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Q: xy lim (x,y)->(0,0) x² + y²

A: We need to write down that the limit exist or not.

Q: 3 3 x³ - y³ z = f(x, y) = x² + xy + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

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Q: :a stream function is given by: Y=2x²y + (x+t)y2 Find the velocity equation for flu me = 1s?

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Q: Use the graph of f to evaluate the following: 6 + f(x) 5 X 4 رها 3 N 1 1 2 4 5 The average rate of…

A: Equation of slope:  Slope =(y2-y1)/(x2-x1) The average change of the function over the given time…

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 7x)y², y(0) = 2…

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Q: 2 ln x + ln (x+1)- 1/2ln (x^2+1). Compress the logarithmic expression.  PRE-CALCULUS HW question..…

A: The given expression,   2 lnx+lnx+1-12lnx2+1

Q: Q1/ Find -1 s² (s+1)(S-1)²

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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

Q: Find an explicit solution of the given initial-value problem. 없을 y(7) = 7 1

A: Find an explicit solution of the given initial-value problem.         dydx=y2-1x2-1  ,    y7=7

Q: Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where…

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Q: Find the solution of the given initial value problem in explicit form 1 y' = (1 - 5x)y², y(0) = 9

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Q: Consider the region R bounded by the curves y = 2 sin(2x) and y = 0 in the interval [0,1] with a…

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Q: Find the general solution of the given differential equation. y' + 3x²y = x² y(x) = Give the largest…

A: The solution is given in the next steps.

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Direction: Solve the following problem of bounded areas, marks for complete work out and mark for…

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Q: Find the solution of the given initial value problem. ty' + - 2y = sint, y(7) = 5, t > 0 y =

A: For the linear differential equation of the form: the general solution is given by: where

Q: 1.  Create a system of linear equations with three equations and three unknowns.     Solve the…

A: The objective is to solve the above question.

Q: 27. The factor = T/2 is multiplied in the evaluation of Wallis formula, where m and n rs of sin and…

A: The factor θ=π2 is multiplied in the evaluation of Wallis formula where m and n are power of sin and…

Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

A: This question is related to vector integration ,we will solve it using given information.

Q: Sketch each of the following: . the solid E • the projection of E onto the xy-plane the projection…

A: answer is in next step.

Q: State the order of the given ordinary differential equation. d²y dx² dy = 1+ dx. Determine whether…

A: We know that :-  The ORDER of a differential equation is the order of the highest  derivatives that…

Q: x-2x + x = 15; x (0) = 7, x (0) = -16 hand written plz

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Q: Initially 100 milligrams of a radioactive substance was present. After 4 hours the mass had…

A: This question is based on application of diffrential equation.

Q: Find the value(s) of k that makes the given function continuous. 4x 5 if x < k f(x) = { = x++1 ifk…

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Q: Given a function, Based on the function, S-3 F(s) = 2 S² +6s+13 a) Determine ƒ(t). b) Based on…

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Q: Lesson Performance Task At an amusement park, a person spends $30 on admission and food, and then…

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Q: Given a function, Based on the function, F(s) = 2s +3 s²-2s+25 a) Determine f(t). b) Based on…

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Q: Given the equation z = arctan(x- y²) with the change of variables x=s³-t³ and y=st² + s²t, use the…

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Q: x³ - y³ z = f(x, y) = x² + xy + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

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Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

Q: 8 0-4 [1-4] and B= 0 5-2 5-8 Find AB and BA given A = Find AB. AB=

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Q: Q5) Find dw/dt at the given value foe the following functions 2) w = 2ve* - lnz.x = ln(t+1), v =…

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Q: You have a penny, a nickel, a dime, a toonie, and a loonie. How many different (non-zero) sums of…

A: You have penny, nickel, dime, toonie and loonie  How many different sum of money produce