For the function f(x) = 5x² 2x, evaluate and simplif f(x+h)-f(x) h 11

Q: If y=f(x)=7e^x + 3x^4 - 20x - 5, Find the equation of the

A: Using derivative first find slope m,

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

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Q: aluate the integral. [29 tan 29 tan 5x sec 4x dx

A: The given integral is  ∫29tan5xsec4xdx

Q: The integrating factor (IF) of the equation y' - 2ycot2x OA sin2x OB cot2x OC.Lnsin2x D.csc2x OE…

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Q: If (OM-ON) 1/12 - - 5, = ?х M y OA. e5 O B. OC. y5 O D. e-5 O E. -5 then what is the integrating…

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Q: Give the implicit solution of y'=y=xy²e Oe-2x = y²(x²+c) O e ²x = y²-c O e²x = x²(y²-c) е…

A: We will find the required  solution of given differential equation.

Q: Use the Law of Cosines to determine the indicated angle 8. (Assume a = 126.5, b = 59.5, and c = 159.…

A: Given, a=126.5, b=59.5 and c=159 Aim: Find θ

Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: 30. If f(t) = sec t, find f"(π/4)

A: Topic- Double derivative of a function. we are given f(t)=sec t and we know that ddtsec t=sec(t)…

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Given half life of 34 hours Initial does of 75 mg

Q: Which of the following equations can be made into a linear diff O A. (x² + xy)dy - (lnx - Iny)dx = 0…

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Q: Find the equation of the plane containing the points P(3,1,5), Q (-1,-1,-1) and R (-2, 2, 4)

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Q: Which of the function is not an exact equation of the first order? OA (e³ + ycosx)dx + (xe³ + sinx +…

A: If a first order Mdx+Ndy=0  is exact then  ∂M∂y=∂N∂x.

Q: The Cartesian coordinates of a point are given. (a) (b) (4,-4) (i) Find polar coordinates (r, 0) of…

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Q: 5 (lx-21-4) dx

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Q: Question 26 Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x =…

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Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0 when…

A: uation Given differential equation of the formMdx+ Ndy=0

Q: Determine the order and degree of the differential equation, 3x- dy4 O A. First order, fourth degree…

A: Topic- Order and degree of differential equation We are given, 3xd4xdy4+5x2d2ydx23-xy=0We know that…

Q: A baseball diamond is in the shape of a square with 50 ft sides. How far is it from home plate to…

A: A baseball diamond is in the shape of as quare with 50 ft sides. To determine how far is it from…

Q: lim h→0 f(−4+h)-f(−4) h

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Q: f(x)=(2x+1)^4. A) Find an equation for the tangent line to the graph of ff at x=2…

A: Givenf(x)=(2x+1)4

Q: Which of the function is not an exact equation of the first order?

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Q: 9. A block of ice, in shape of a right circular cone, is melting in such a way that both height h…

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Q: √6 + 2x² lim x→∞ 6 + 10x [ZX][][+] [94] lim x-→-8 6 + 10x || ||

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Q: 4. Find the limit. lim x-0 lim X-0 5+5x+ sin x 6 cos x 5+ 5x + sin x 6 cos x CA. Yes, lim f(x)…

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Q: So the system of equations by using the inverse of the coefficient matrix if it exists and by the…

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Q: Related Rates 8. A thin circular metal disk changes size (but not shape) when heated. The disk is…

A: Let radius of disk = r mm Area of circular disk =πr2 mm2

Q: Let f(x, y, z) = xy² + z and x = s²t³, y = st, and z = = $³4³. (a) Calculate the primary derivatives…

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: Eliminate the arbitrary constants of y=c₁e*+cx*— sin3x

A: We use differentiation to Eliminate the arbitrary constant, we differentiate the given equation as…

Q: A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the…

A: Given :- dNdt=-0.069N

Q: 3. Find lim f(x) and lim f(x) for the given function and value of c. Tough X-C+ X-C f(x) = (x+8)-…

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Q: What is the value of k so that the differential equation (y³ + kxy4 − 2x)dx + (3xy² + 20x²y³)dy = 0…

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Q: Derive a Differential Equation that is free from arbitrary constants: y = Ae²x + Bxe²x

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Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. 3x O A. O B. C. D. O E.…

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Q: Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x - sinh…

A: We need to rewrite the given expression in terms of exponentials.

Q: Use the Binomial Theorem to expand and then simplify the result: (x2 + x + 1)3.

A: Given expression: x2+x+13

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4e³ − x²y² – 3x)dy = 0 when…

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: To solve for the value of constant C in  the equation: 2x+3y'=y+2x+312when x=-1, and y=0.

Q: If 2 = (x + y)e*, x = 3t, y = 4-t², find dz/dt using the chain rule. Assume the variables are…

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Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: what is decreasing function?

A: What is decreasing function?

Q: Determine the degree, order, and whether it is linear or non-linear (y") ³-4y²=105x

A: Determine the degree,order, and whether it is linear or non linear

Q: The degree of homogeneity of the function f(x, y) = (x² − 4y²)-¹/² O A. 1 OB.-1 O C. -1/2 D. None of…

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Q: hich of the following equations can be made into a linear differential equation? DA. (x² + xy)dy -…

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Q: Show that:

A: Given, nr+nr+1=n+1r+1

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

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Q: parts remaining Evaluate using integration by parts or substitution. Check by differentiating. (3x²…

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Q: 4. Let sin² x + cos² y = x² + y². Find y' by using implicit differentiation. ។

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Q: Find the explicit solution of dy/dx=2xy² + 3x²y², y ( 1) = − 1 O 1/y=3-x²-x3 Oy=x²/2+x²³/3-3…

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