Use the Chain Rule to find dz/dt. z = tan−1(y/x),    x = et,    y = 5 − e−t

Q: 3. X+Y)/4=5Z

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Q: mplete the description of the piecewise function graphed belo 6+ 5

A: Here we have to complete the description of the piecewise function graph below.

Q: Can someone explain tangent for more as well as limits. *all of this within calculus *

A: Please see the below picture for detailed solution.

Q: Write a function of the form f(x) = csc (Bx-C) for the given graph. 3 2 1 0 -1 -2 -3 F 12 5п 12 3πI…

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Q: Prove that tan'z= let% 1/2 in (1+2) ة لله tan't Z • tanw=Z Z = Sinw cosw

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Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: 7. A traditional first experiment in a physics laboratory is to make 98 observations ab records the…

A: Given formula for linear regression is as below  take t as x and h as y. find mean value

Q: Suppose ū = (–5, −4, −5) and v = (–2, 4, −5). Then u x vis Uxuis and

A: Topic- Cross Product of Vectors

Q: lim x → 0 cosx−1 -1 X

A: The given limit is: limx→0cosx-1x   As we know that; cos-θ=cosθ

Q: Use the final value theorem, the final value of f(t) = 6. (et +2) - 10 is .....

A: final value theorem

Q: speed x HOSX< 1000 if Graph Ffor 0 sx s 100. F sxs F 1000 (100, 1000 (100, 1000

A: We have to make the function from given data and graph the function.

Q: Consider the method of Variation of Parameters for solving the general linear equation of first…

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Q: 7. Find all constants a, b that make f continuous at x = 2. (Use limits and definition of…

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Q: For each statement,write true or false {0,2,6}={6,2,0} {2,3,4} =[2,4] {XER:0≤x≤6}= [0,6]…

A: We will  state whether the statement is true or false.

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: 1. (Section 14.1) Graph the curve given by vector function 7 (t) = of positive orientation. Do not…

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Q: domain

A: Please refer to the image below

Q: (19))2a² = -6 +8a

A: solve quadratic equation by completing square 2a2=-6+8a

Q: Given f(x) = 19xº sinx+12x−7, find f'(x). f'(x) =

A: Concept: Differentiation: The slope of the tangent to the curvey = f(x) at (x, f(x)) is the…

Q: Find the shortest distance between the (entire) line L1 passing through the points A(1, 1, 2) and…

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Q: Find the limit. Enter the exact answer. If the limit does not exist, enter NA. 5x2 – x – 4 lim x→1…

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Q: If a = (1, 2, 1) and b cross products. 1. a × b : = 2. b xa = = (12, 15, 1), find the following

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Q: Find a parameterization for the curve shown in the figure below. r(t) = where = -1 1,0 -1 <t<

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Q: Use the graph to find the average rate of change. 5) Monthly Cellular Phone Charge in Dollars 80+…

A: To find average rate of change of given function through its graph.

Q: C. Find the standard form of the equation of a circle given the following conditions. 11. Radius is…

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Q: Evaluate the following integral. 6 x (x² + 5)² dx Find the partial fraction decomposition of the…

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Q: H] Example: If an amount of $5000 is invested at 3% compounded quarterly, what is the amount after 3…

A: Note:- since part f incomplete to find value of x we need equations of revenue function and cost…

Q: Solve the given equation on the interval 0 ≤ 0 ≤ 27: tan 0+1=0

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Q: Use an appropriate Pythagorean identity to find the indicated value. Write your answer as a…

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Q: Z(A+BZ²) The Z-transform of the following function f[k] =2.2+(-5)*-(-4)* i (Z-2)(Z+1)(Z+5) so the…

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Q: 13. The rate at which a garden uses water is measuued in thousands of gallons. If the usage rate is…

A: I am attaching image so that you understand each and every step. Given data:- The rate at which a…

Q: Given s(t)=t² + t, find (a) v(t). (c) the velocity and acceleration when t = 4. (b) a(t). (a) v(t) =…

A: Concept: The instantaneous velocity at a given time is the derivative of a function that represents…

Q: onsider the function in the graph to the right. he function has a maximum of at x = The function has…

A: From the given graph

Q: 2. lim f(x) = | x-1 lim f(x) = 1 x1+ lim f(x) = | f(1) = |

A: 2.According to graph limx→1-fx=1limx→1+fx=1limx→1-fx=limx→1+fx=1there fore limx→1fx=1    limit exist…

Q: y' xe2y subject to initial condition of y(0) = -1 =

A: Please see the below picture for detailed solution.

Q: Evaluate: lim tan3x x→0 x

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Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

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Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

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Q: Find the solution of the differential equation (6x² − y + 3) dr+ (3y² - x - 2) dy=0 1 O x + O 2x³ O…

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Q: Solve the inequality involving absolute value. Enter the exact answer in interval notation. To enter…

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Q: Sketch

A: Please refer to the image below

Q: lim t→l 1+√t+ √t+√t t² + 1 + 1 t³-2

A: I have solved step by step in detail...and I have written answer up to simplified…

Q: A positive angle less than 360° that is coterminal to -111° is

A: To find a positive coterminal angle, one should add 360o to the given angle.

Q: (b) part of parabola y = −2x² from (−1, −2) to (2, —–8)

A: Given Equation of parabola y=-2x2 from -1, -2 to 2, -8.

Q: The circumference C of a circle is a function of its radius given by C (r) = 2πr. a. Express the…

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Q: se the isosceles right triangle and the 30°-60°-90° triangle to complete 45 r √2 - 45 60⁰ 30% √3

A: Part 1 :  For triangle                  For θ=30° It is right-angled triangle.…

Q: o this typewritten only for upvote no upvote for handwritten skip if you already did this…

A: Given,Diameter=12 and Passes through points (8,1) and (2,-5)radius r= diameter2=6General Equation of…

Q: Evaluate ex+y dx dy In8 1-y y=0x=0 O e-In2 eln 8-7 025

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Q: ● जे

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Q: Consider 3 4+2³ (a) First, define this as a Mathematica expression and compute the third derivative.…

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