Let f(x) = m = 6 mx x² + 7x ,2 if x < - 4 - 4 2 if x > If f(x) is a function which is continuous everywhere, then we must have

Q: If x = √x^5y^5 + x^2y + xy^2, find:   zy zxy

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Q: For the curve: f(x) = 3x^2- 12 : i. determine the x and y intercepts.  ii. locate the stationary…

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Q: Question 11 Solve the differential equation A) Iny=c B) Inc-y=x c) Iny-x=c (D) x+Iny=c dy dx

A: See the details solution in below

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Q: Refer to the graph of y = f(x) = x² + x shown. a) Find the slope of the secant line joining (-2,…

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Q: Find the general solution of the differential equation y (iv) + 2y''' y '' — 2y'=0.

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Q: Find the general solution of the Differential Equations: dy dx 3)(x+1). 3x · y = e³x (x + 1)²

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Q: Real limits are important whenever you are measuring a(n) O independent O dependent Odiscrete O…

A: Solution: this is one liner answer Ans continuous

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Q: 00 n=( 3n + 2 5n3+1

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Q: Parametrize the intersection of the surfaces y² − z² = x − 5, y² + z² = 9 using trigonometric…

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Q: How did you go from x^5 to x^10 on the denominator? You divided everything by x^5 and then just the…

A: Limx-infinity(x3-3x5+5)/sqrt(x4+12x10+1).

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A: Let 1-x = t

Q: 11. 2n+1 ΣΕΡ 201 n=1

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Q: Use implicit differentiation to find d'y dx² d'y if 2x² - 3y² = 4. dx²

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Q: PROBLEM 3 [COMPOSITE AND INVERSE FUNCTIONS]: Two functions p(x) and q (x) are inverses of each other…

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Q: 2 Suppose that lim f(x) = -73. == to Blamk 1 D+X lim g(x) = 4, and lim h(x) x-a = . The lim x→a…

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Q: Solution limx→ Steps limx→ (arctan(x)) (arctan(x)) 88 || - Apply the common limit: limx. Show Steps…

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Q: Use symbolic notation and fractions where needed. Give your answer as the coordinates of a point in…

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Q: Consider the planes given by the equations 3y - x - 4z = 3, x - 2y +z = 4. (a) Find a vector u…

A: Given that equation of plane 3y-x-4z=3x-2y+z=4Solution :-x+3y-4z=3 x-2y+z=4normal vector of plane 1…

Q: Find L-1 (s+2)2+16 2+16³.

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Q: Let g(x) = cos(x), and h (x) = -3x4 - 17x³ - 4x² +92x + 113. If f is a function such that g (x) ≤…

A: This is a problem related to sandwich theorem of the limit. Please follow the procedure given below.

Q: Let f and g be functions defined by f(x)=x²+2x+2 and g(x)=x2-1 Consider the two statements I and II.…

A: The functions are given by fx =  x2+2x+2gx = x2-1The statements are I. The rational function fxgx is…

Q: 4) Find the following by using the substitution z = tan cos e de ii) sine cose + sin € dx ii) 1+ sin…

A: As per the guidelines I am supposed to do the first question among multiple questions, so here I am…

Q: Question 9 Which is equivalent to Inlyl=3x + Cwhen y is solved in terms of x? A B y=ce²x y = 3x + C…

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Q: Find the equation for the tangent line of the graph of y = x² at (-1, 1). Equation: 1

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Q: In a binomial situation, q = 1 - p. O True O False

A: Solution ) in the binomial situation there are two possible events  p = probability of each success…

Q: Find the common difference and the 100th of the arithmetic sequence   If a5 = 6 and a14 = 42

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Q: Find a and b such that f is differentiable everywhere. 8 cos(x), x < 0 ax + b, X 20 a b = || f(x)

A: Since the function is differentiable everywhere so it will be differentiable at x=0

Q: 3. Parabola vertex at x-axis, open to the right and the length of the latus rectum and the…

A: 3.We have to find the differential equation of the given parabola.

Q: Find such that the function C (x² - 6 x ≤ c f(x) S C 10x 31 x > C is continuous everywhere.

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Q: √²³(2x − 1)³dx -

A: As per guidelines we can answer only one question at a time. So if you need more answers kindly…

Q: 2) If f(x) = x - 5 and g(x) = x² + 3; Find the following: [g(f(x)), g(g(x)), f(f(2)), g(g(-5))]

A: We have to find the composite functions.   According to our guidelines we can solve only one…

Q: Verify that the conclusion of the Clairaut's Theorem holds a) z = sin(xy) b) z = sin(x - y) c) z =…

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Q: a. Construct a rational function whose only asymptotes are y = 4 and x = 1, and whose à intercept is…

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Q: 33. f(0) is undefined. lim f(x) = 4 x-0 ƒ(2) = 6 lim f(x) = 3 x-2

A: This is a problem related to graph of the limit function. Please follow the procedure given below.

Q: A thermometer is taken from a room where the temperature is 21°C to the outdoors, where the…

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Q: dy/dx=2y/x+1

A: As we know that; The standard form of the first order linear differential equation is: dydx+Pxy=Qx…

Q: Homework: Evaluate the following integrals: Please, expert, I do not have money and my financial…

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Q: Question 1 The differential equation y - 2y - 3x2=0 is linear and homogeneous. A FALSE B) TRUE

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Q: An equation for the line tangent to the graph of the differentiable function f at x = 3 is y = 4x +…

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Q: 10. Find the amplitude (a) and period (T) of the following function f(t)=2cos(720xt-6)

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Q: Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

A: A sinosoidal curve can be view as y=Asin(kx)+C, where A is the Amplitude, k is the period, and C is…

Q: respect to x without using the formula. Use y instead of show differentiation. Use / for fraction,…

A: we will find the required.

Q: What is the order of the differential equation x2dy/dx-2xy"=0?? (A) 1 (B) 2 C) 4 (D) 3

A: Order is given by the highest derivative present in the differential equation.

Q: 2 P(x)=x-5x + 2x+8 = (x − 4)(x − 2)(x + 1)

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Q: Let L₁ : x=1+t, y=−2+t, z = 2t; L₂ : x=2+s, y=3-s, z = s If the lines are skew, find the equations…

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