Find the domain and the range of the function. (Enter your answers using Interval notation.) h(x) = -√√x+8 domain -8,00 range -00,00

Q: 1 For the parametric curve * = find an equation for the tangent line to the curve at the point…

A: To find equation of tangent line:

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: Solve the following ODES by Undetermined Coeff D Ş 17 4X y - 16 y = 19.2 € + 60e, y(a) = ý (0) -4X…

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Q: Show that the function f(x,y) = 8x²y subject to 3x - y = 9 does not have an absolute minimum or…

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Q: Write an equation for the function graphed below. The y intercept is at (0,-0.2) -7 -6 -5 -4 -p 2 y…

A: To find the equation for the function.

Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x>0x2-1if x≤0

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Q: Use the substitution t = -x to solve the given initial-value problem on the interval (-∞o, 0) x²y" -…

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Q: How did you get 6?

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Q: the particular Solution is 1 84-1 2. = 2. 1 04-1 — (ex) - 1/₂₁ (2x), D4-1 = LYDB (ex) = 4p3 De_…

A: Given D4-1y=2 sinhx+sinx The auxiliary equation is m4-1=0⇒m22-12=0⇒m2-1(m2+1)=0 Therefore m= ±1, ±i…

Q: calculation for P.I ур cos²x D²+1 2 2 cos²x D² + 1 1 {3 2 21 - 1+ cos2x D² + I HOW DID HE GET THE…

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Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: Write an equation for the function graphed below 5+ 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 y = -5+ 1…

A: topic- graph of a function

Q: Tutorial Exercise Find the domain of the function. 7 |x²-161 g(x) = Step 1 The domain is the set of…

A: To solve the given domain problem of the functions.

Q: 14-13-12-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Find an equation for the graph above. 4+h(t) 27 2 1 2 -2-…

A: The given graph is:   Consider the function is: y=AsinBx-C+D From the given graph, the maximum…

Q: Write the given differential equation in the form L(y)- 90x), where L is a linear 4y"-15y4ys…

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Q: 8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

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Q: - The complementary function is १ex . Ус where C₁, C₂, C3, C4 си the particular Solution se = c₁ex +…

A: This is a problem of ODE. Please follow the procedure given below.

Q: . Find the open interval(s) on which the function is increasing and decreasing.

A: Given :f(x)=9x3-11x

Q: 5. [tan³x sec³x dx

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Q: Sketch the region R whose area is given by the iterated integral. To Se *6 *3 7- 6- 5- 4- 3- نيا 2-…

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Q: Hello! Can someone help me solve both A and B. Thank you! Please show all work, as i keep getting…

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Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: 1. [cos³x dx [Use the reduction formula]

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Q: a. b. algal dy dx dy dx + y = xy³ - y = ex y² -X

A: See this solution in below.

Q: 23. Express each of the following as a logarithm. Use a calculator to evaluate your answer correct…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

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Q: Let R be the region below the curve y = 4x², to the left of above the x-axis. Find the centroid of…

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Q: Find an equation of the tangent plane to the surface at the given point. (2,0,0) g(x, y) = arctan…

A: Answer and explanation is given below...

Q: 10. rectangular box with a square base and open top must have a volume of 4 m³. Find the dimensions…

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Q: 2. The function ƒ(x) = x² − 4 is transformed to g(x) =— (x² − 4). Compare the domain, range,…

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Q: Integrate using the fundamental theorem of calculus

A: Our Aim is to evaluate the integral given below using Fundamental Theoem of Calculus.∫01x4+12 dx…

Q: Write an equation for the function f(x) shown. The leading coefficient is 1.  Asymptotes: y=-1 x=…

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Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" +…

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Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

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Q: ((x)/)6 (1) (e) f(g(x)) ((7-))* (P)

A: Given;  f(x)=2x3 and g(x)=4x+5.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Match the differential equations and the description/s that is/ are true to the differential…

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Q: QUESTION 1 P 0 0 9 0 00r Show that 0 Hence, determine the inverse of the following matrices: 100 i.…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

A: We will use standard method to solve this.

Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).

Q: O O O O O IfE is the solid hemisphere a² + y² +2²5 49 and y 20, set up the integral using spherical…

A: Solution: In converting to spherical coordinates, we use so that

Q: How much must a person save monthly at an interest of 7.3% to buy a $15,000 car in five years?…

A: We have to find the monthly amount to save.

Q: z²i+xzj+ye² of the sphere x² + y² + z² Given F = 2 [[ S 50 that lies inside the cone z = √x² + y²…

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Q: Find the general solution of the given second-order differential equation. 9y"+y' = 0 y(x) =

A: General solution of real roots is used.

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.