1. Determine the domain and range of the vector-valued function r(t) = (√t+3, In(2 – t), t²)

Q: Divide using long division. State the quotient q(x) and the remainder r(x) 8x cubed - 5x squared +…

A: Solution- Given Dividend=8X3-5X2+9X+2 Divisor = 8X2+3X+5 remainder =? quotient q(x)=?   by Long…

Q: Suppose that the temperature of a metal plate is given by T(x, y) = x²+2x+y², for points (x, y) on…

A: Given: The temperature of a metal plate is given by T(x,y)=x2+2x+y2 for points (x,y) on the…

Q: Fill in the blank. The symbol C, represents a constant. Write this result as a linear first-order…

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Q: Question Estimate (4x² + 3) dx using the midpoint rule and 4 subintervals. Enter an exact value.…

A: To evaluate: ∫024x2+3dx Let fx=4x2+3 Now, interval is from 0 to 2 We have 4 subinterval, therefore…

Q: By about how much will f(x,y,z) = In√x² + y² +2² change if the point P(x,y,z) moves from P(6.5.15) a…

A: NOTE: Refresh your page if you can't see any equations. . the given direction vector is find its…

Q: 2. Match each logarithmic function with its graph. I II ++ (a) f(x) = log₂ (x) (b) f(x) = -log₂ (-x)…

A: We have given equation and graph to match From given graphs graph I :   (a)  fx=-log2x graph II :…

Q: Find the angle of inclination θ of the tangent plane to the surface 2x2-3y2+z=0 at the point…

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Q: lim 8e +71-8 2e¹+3r-2

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Q: Find f'(x). f(x) = 9x-8 4x+9

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Q: Question 1 i) ii) iii) iv) Find the derivative of the following function using the first principle:…

A: i) f(t)=3t2+2t+1 Using the first principle: f'(t)=limh→0f(t+h_)-f(t)h…

Q: The volume V of a fixed amount of gas varies directly as the temperature T and inversely as the…

A: Given: the volume V varies directly as the temperature T and inverselyas the pressure P.Therefore, V…

Q: Graph the following. 0 0 peacewise function. +£3. 3≤ t < 5 + 25

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Q: (a) Find the differential dy. y = √3+x² dy= X 2 √3+x² dy = -dx (b) Evaluate dy for the given values…

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Q: Find the following derivatives. Express your answer in terms of the independent variables. Ws and w,…

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Q: . Find a particular solution Y(t) of y" — 2y" — y' + 2y = e²t

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Q: Solve the differential equation. dy dx 6x²y² for y # 0

A: Note : As per our Guidelines , we can solve first question .Please Repost remaining question .

Q: Describe the triangular region whose vertices are at (0, 0), (1, 0), (1, 2) as set in the polar…

A: Answer is in step 2.

Q: Find the gradient of the function at the given point. Function Point f(x, y) = x + 2y (1, 3) y + 1…

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Q: Evaluate the limit analytically (that is, without using a graph or table). x² + 11x + 24 x + 3 lim…

A: We solve the given limit by factoring numerator and after that simplifying common factor with…

Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=√56x²-9y²-16x-31…

A: The function is given as , fx,y=56x2-9y2-16x-31+1-8x find the local minima , local maxima and saddle…

Q: ************** A cylindrical package to be sent by a postal service can have a maximum combined…

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Q: #3) Find the derivative of the function. y = 2-5x

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Q: Suppose a tank initially contains 1000 gallons of water and that the rate of change of its volume…

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Q: Use linear approximation to approximation (sqrt√36.1) as follows. Let ?(?)=(sqrt√x). The equation…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A: We can find the particular solution in the below steps using the appropriate method.

Q: Given the following functions, find each: 2 f(x) = x² - 9x + 18 g(x) = x - 3 (f + g)(x) (f - g)(x) =

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Q: (a) point The graph of the function f(x) = 3²- can be obtained from the graph of g(x) = 3* by one of…

A: Let's find which transformation is used in given function.

Q: For the function f(x) = -3 sin(x two periods. Enter the exact answers. For the number 7, either…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (a) We have 3 X Y

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Q: what is an improper integral?

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Q: Graph f(x) = X (G) O A. and g(x) = log 1/8x in the same rectangular coordinate system. Choose the…

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Q: f(x) = x² - 11x + 30 g(x) = x - 5 (f+g)(x) = (f- g)(x)

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Q: What is the equation of the tangent line to the curve of y = A 2x+9y+1=0 D. 9x+2y+1=0 B. 2x-9y-1=0…

A: Topic = Derivative Correct Option = C

Q: 191-21-A 20 VV 10 -2 -4

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Q: f(x)=ln|sec

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Q: A van is traveling due north at a speed of 80 km/h. If the van started off 7 km directly east of the…

A: Solution:

Q: The number of inhabitants y in a city increases according to the relationship y=50,000+1500x. x…

A: The given equation is:- y=50,000+1500x   Comparing with the standard equation:- y=kx+C   C = 50000 k…

Q: Question Find the actual value of t 1 dx, then 3√x approximate using the midpoint rule with four…

A: Here we have given a definite integral now we have to solve this by using midpoint rule. And also we…

Q: Find the exact value of the given expression. tan(cos-¹(²)) 2 3 4

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Q: Find lim h(x), if possible. (a) h(x) = f(x) = -8x² + 3x - 4 f(x) X lim h(x) (b) h(x): f(x) lim h(x)…

A: Concept: A function may get close to two distinct limits. There are two scenarios: one in which the…

Q: 41. lim [2ln(x-3) - In(3x² + 5)] X-80

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Q: Given that f(x) = x² - 13x and g(x) = x + 13, find (a) (f + g)(-4)= (b) (f- g)(-4)= (c) (fg)( 1) (4)…

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Q: If tant = what is tan (t - π)? Enter the exact answer. tan (t = π) = - 囡囡

A: Concept: The formula of tan(a-b) is tana-b=tana-tanb1-tan(a)tan(b)

Q: Suppose that the following equation defines y as a differentiable function of x: y = arctan(x²y).…

A: NOTE: Refresh your page if you can't see any equations. . take derivative use the derivative rule…

Q: Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate…

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Q: Find the indefinite integral. (Use C for the constant of integration.) sinh(1 − 6x) dx

A: The given integral: ∫sinh1-6x dxWe need to evaluate the indefinite integral.

Q: Find the exact value of sin sin (*) 4) = (4) 团团团 EESTIMENT

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Q: Use the chain rule to find the indicated partial derivatives at p=4, r = 3,0 = 0 and enter them into…

A: given u = x2 + yz x = prsinθy = prcosθz = p + r

Q: Evaluate the following integrals and state that they diverge or converge.

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