Determine the maximum and minimum points of the given functions below. h(z)=4z3−3z2+9z+12

Q: Find the limit of the following functions x 5 +3 x3−2 as x→2 X3 +4/X-4  as x→4

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Q: 4. Find the derivative. x? + 6x – 5 (a) 5х -1 (b) ƒ(x) = (3xr² – 5x - 7)' Us e chain rule (c) y =(x-...

A: Topic:- derivatives

Q: What is the amplitude and period of the function f(x) = cos(6x)? Provide your answer below:

A: for f(x) = Acos(bx)amplitude is given by Amplitude: Aperiod is given by   p = 2πa  

Q: 5. Find the volume of the solids generated by revolving the regions bounded by the curve y = sec y =...

A: Here, the region bounded by the curve y=sec x, y=0  from x=-π4 to x=π4 about x-axis is:  

Q: 4. Evaluatelim X-1 Show your complete x-1 solution.

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Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where...

A: Plane

Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. fx.y) = - 2 + 7xy - 6...

A: We have to find the maxima and minima of the function.

Q: Solve the problem. Evaluate at (x, y, z) = (2, 5, 3) for the function u(p, q, r) = p 2q 2- r; p = y ...

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Q: Find the derivative of the function y = (cot x- csc x) 1 %3D dy %3D dx

A: ddxcotx-cscx-1

Q: dy 1 6y'z da y (1) = = 25

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Q: Use the Chain Rule to find the indicated partial derivatives. R = ln(u2 + v2 + w2), u = x + 7y,   ...

A: Given that R=lnu2+v2+w2u=x+7y , v=4x-y, w=4xyTo find :∂R∂x,∂R∂yR=lnx+7y 2+4x-y2+4xy2∂R∂x=1x+7y 2+4x-...

Q: 5. Prove that lim Show your t→-2 t+2 complete solution.

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Q: Find the derivative of y with respect to t. 1 y3D cot dy dt %3D

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Q: If g = 1110°, simplify the expression sin- (sin g). If undefined, enter Ø. Provide your answer below...

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Q: The diameter of a sphere is measured as 100 ± 3 cm and the volume is calculated from this measuremen...

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Q: Simplify the expression tan (sin- (-)). Provide your answer below:

A: Given that tansin-1-1237Solution :tansin-1-1237tan-sin-11237       sin-1-θ=-sin-1θ-tansin-11237     ...

Q: Find the derivative of the following functions using the definition of the sine and cosine function....

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Q: 1. For function z = f(x, y) where f(x, y) = 4 – x² – 2y², we compute that fa(1,1) = -2 and fy(1,1) =...

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Q: 8. A company is increasing production of oven mitts at the rate of 4 per day. All oven mitts that ar...

A: Revenue function , R (x) = x P(x) Where P is the demand function  and x is the  price per unit.

Q: Homework: Graph the following functions and show domains and ranges of them. 1+cos2r 1. 3. y = cot3x...

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Q: 1. Engineers have observed that when transferring a message I (an input signal) through a physical m...

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Q: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

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Q: Find the set of solutions for the linear system + 3x2 3x3 -10 %3D X1 X2 4x3 -3 4x3 -8 Use s1, s2, et...

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Q: The temperatures T (in °F) at which water boils at selected pressures p (in pounds per square inch) ...

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Q: (6)The radiusr of a circle is increasin g at the rate of 8 cm per min ute. Find the rate of change o...

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Q: Calculate the average rate of change of the given function f over the intervals [a, a + h] where h =...

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Q: fa- (4 – 3 cos x) sin? x dx

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Q: Identify what law(s) are being used in each step: (p ^ q) → (p V q) (p A q) → (p V q) =T = - (pA q) ...

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Q: gien oferdone (D- JI) (D +3I); the to the grven finctions e-3%

A: (D-2I)(D+3I)=D2+3D-2D-6I=D2+D-6I Apply the operator on e2x (D2+D-6)e2x=D2(e2x)+D(e2x)-6e2x=D(2e2x)+2...

Q: Find the derivative of the trigonometric function. cot(x) f(x) sin(x) f'(x) = Need Help? Read It Wat...

A: Given that       f(x) = cot(x)/sin(x) 

Q: For what values of x d X = II

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Q: Find the derivative of the given function. y = x-5x +5) y = (x² - 5x + 5) e 6x 15 dy dx

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Q: dy Use implicit differentiation to find dx 7xy + y = 9x+y

A: Given 7xy+y2=9x+y To find dydx:

Q: Test the series below for convergence using the Ratio Test. 97 n! n=1 The limit of the ratio test si...

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Q: 2 + 4 2X = 3

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Q: Write a chain rule formula for the following derivative. for u = f(p, q); p = g(x, y, z), q = h(x, y...

A: Given problem:-

Q: Evaluate the integral. 2 dx 5 Vx (3 +2x)

A: We will solve the integral by substitution method. By (3+2√x)=t

Q: Test the series below for convergence using the Root Test. 8n 4n + 1 n=1 The limit of the root test ...

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Q: Let f(x) = x8 - 8x6. When the tangent line is vertical, what is the derivative of f(x)?

A: Here we will understand the vertical tangent line and we will find derivative of given function,

Q: for an equivalence relation R on A, both sets, the class of equivalence classes of R —A/R— is a set.

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Q: 1. Graph the line using parametric equations from t = 2 tot = 6. x = 10 – 2t, y = 3 – ÷t

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Q: The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is giv...

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Q: Use the price-demand equation below to find E(p), the elasticity of demand. x= f(p) = 40,000 - 550p ...

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Q: At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing no...

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Q: Solve the following equation to determine if f (x) is continuous given the function: f (x) = 6x+7  ...

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Q: Find the general solution. (x³+3xy²)dx + (y³ +3x²y)dy=0 O a. x4-y4-6x²y² = c О а. O b. x*+y*+6x?y? =...

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Q: The path of a total solar eclipse is modeled by f(t) = 0.002311 - 0 506t + 40 266, where f(t) is the...

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. 1...

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Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans ...

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Q: Find the solution of the equation 4xsinx +2 cos 2x a2 2 using the Newton-Raphson method with an erro...

A: Given: