y --5 -4 -3-2 -2- -3- lim f(x) x-2

Q: Simplify the expression: 2(-5) - (-3)(4)

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Q: Please answer the following question.

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Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on lim...

Q: Find the derivative of the trigonometric function.

A: The given function is y=31-sinx2cosx

Q: Evaluate each limit. (4х + 10 lim xS2 2х - 2

A: limx→24x+102x-2

Q: The dimensions of a closed rectangular box are measured as 90 cm, 69 cm, and 26 cm, respectively, wi...

A: Given that: The dimension of a closed rectangular box is 90 cm, 69 cm and 26 cm respectively. So, L=...

Q: sketch the phase portrait of the given system for −2 ≤ x ≤ 2, −2 ≤ y ≤ 2. Comment on the types of eq...

A: Consider the given differential equation: x'=x-2y+5xyy'=2x+y Here, the objective is to sketch the ph...

Q: Compute the following double integral over the indicated rectangle.

A: Given: ∬sin2x-11+6ydAR and R=π4,π2×0,1 To find: The value of integral.

Q: Use properties of limits to find the indicated limit (as shown). It may be necessary to rewrite an e...

A: Given that limx→1x2+2x-3x2-1. Compute the limit as follows.  

Q: Find the limit

A: The given expression limx→013+x-13x

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence con...

A: an = −3−n We need to determine the convergence or divergence of the sequence with the given nth term

Q: Use the definition of partial derivatives as limits to find f(x, y) and fy(x, y). f(x, y) = 6xy2 - 6...

A: Consider the function: fx,y=6xy2-6x3y To calculate partial derivatives with respect to “x” using the...

Q: Determine the amplitude and period of y = -4cos ᴫx/2. Then graph the function for -4 ≤ x ≤ 4.

A: Given y=-4cospix/2 . We need to find amplitude and period of the wave. The general representation of...

Q: A given bacteria culture initially contains 2500 bacteria and doubles every half hour. The number of...

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Q: Evaluate the following integrals.

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Q: Complete the following statement. If dy/dx is large, then smallchanges in x will result in relativel...

A: According to the question, we have to complete the statement, If dydx is large, then smallchanges in...

Q: Use the definition of continuity to determine whether f(x) = 2x + 5 at a = 1.

A: Given function is fx=2x+5.

Q: Let g(x)= 5 - 5x + 4x2 then the expression (g(x+h) - g(x))/h can be written as Ah + Bx + C, where A,...

A: Given: g(x)=5−5x+4x2

Q: In Exercises 45–48, calculate the derivative using the values: f(4) f'(4) 8(4) g'(4) -1 10 -2 5

A: Calculate the derivative F'4,wher F(x)=x2f(x)We are given f(4)=10f'4=-2

Q: A 13 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding dow...

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Q: Integration review Evaluate the following integrals.

A: We have to evaluate I=∫lnw-17lnwwdw Let substitute  u=lnw-1 Differentiating both sides with respect ...

Q: Simplify (assume X>0) √(48x3) / √(3x)

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Q: Obtain a Vector of mayni tude lo that has the same direction as the Vector pPerpendicular toiboth 2 ...

A: The vector here has a magnitude 10 and perpendicular to both the vectors, 2ax⏞-4ay⏞+3az⏞ and 2ax⏞+5a...

Q: Calculus Question

A: Given function, f(x,y)=ln(x+x2+y2)

Q: Calculus Question

A: Given: a)   f(x)=x+7          if x<0ex         if 0≤x≤15-x         if x>1 b) f(-4)=3 and limx→...

Q: The rate of change of the value of goods exported from a country between 1990 and 2001 can be modele...

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Q: EXAMPLE 6 Slopes of tangent lines Find for the following curves. Interpret the dx result and determi...

A: a). x=ft=t, y=gt=2t Differentiating with respect to t, we get dxdt=1 & dydt=2·12tdxdt=1 & dy...

Q: d {e® + e=®} dx Find

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Q: Use a table of values to estimate the value of the limit. V x + 25 5 lim

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Q: Calculus Question

A: The length of equal sides of the isosceles triangle  l=5cm angle between these two sides =θ+θ=2θ Are...

Q: a. Find the local extrema of each function on the given interval, andsay where they occur.b. Graph t...

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Q: Consider the following. h(x) = x Vx – 7 - 7 Find the critical numbers. (Enter your answers as a comm...

A: Given function: h(x)=xx-73 To find out critical numbers, take derivative and then set it equal to 0 ...

Q: Use polar coordinates to find the limit:

A: To find limit using polar coordinates limx,y→0,0e-x2-y2-1x2+y2

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval...

A: Differentiate x with respect t. dxdt=ddtcos2t=-2sin t cost  Differentiate y with respect to t. dydt=...

Q: Find the differential of the function. z = e ** cos(8nt)

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Q: Let f(x) = √x and g(x) =2-x/2 Find f(g(x)) and write its domain in interval notation.  a) f(g(x...

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Q: I need help with 23

A: To find the slope of the tangent we need dydx dydx=dydtdxdt=ddt(4sint)ddt(3cost)=4cost-3sint=-43tant

Q: d (x dx 미

A: ddxxx10

Q: Calculus Question

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Q: determine the general solution to thegiven differential equation. (D − 4)(D + 2)y = 0.

A: To determine the general solution of given differential equation: (D-4)(D+2)y=0

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.