compute dy/dx using the limit definition. y = 4 − x2

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: Assume y' meand dy/dt. Solve y′′+ 5y′+ 6y= 0, and find the limit as t goes to ∞ of y(t).

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Q: dz/dy for z = e^xy

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Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

A:

Q: Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).

A: I have provided a solution in step2.

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

A:

Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: If y=xtan(x) then dy at x = Tt is: dx

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Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: Let z=e"In(xy), determine dx

A: Solving the problem by doing partial differentiation.

Q: 1²e¹dV where E is bounded by the parabolic cy E

A: the answer is give in step2

Q: Find dydx? for f(x, y) = eXy

A:

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

Q: If the continuous RV X has pdf f(x) = (x + 1), in – 1 < x < 2 and 0, %3D elsewhere, find the pdf of…

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Q: Compute fx, fy: f (x, y) = arctan(xy)

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Find the linearization L(x)of the function at a .

A:

Q: 1. Rewrite the following improper integrals as a limit and then evalute them, or state that they…

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Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: Suppose f(x) is continuous on R such that F(x) is an antiderivative of f(x). Furthermore i Find F(1)…

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Q: Find the limit of function f (x, y)D. at the point (0,0) through the path x=y². а. О b. 1 8 d. does…

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Q: Given D = e* sin y ax – e¯* cos y ay. Find divergence of D. -

A: Calculate divergence: div. ∆=∂∂xe-xsiny+∂∂x-e-xcosy         =-e-xsiny+e-xsiny         =0

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: as f(z) = e e analytic %3D

A:

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: dy If y = tan t , x = tan? t ,Find by using Chain Rule dx at t =

A: Let the two functions are xt and yt. The chain rule to find dydx is given by the following formula.…

Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: The limit of f (x, y) : as (x,y) approaches (0,0): %3D O Infinity O Doesn't exist Exists and equal…

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Q: dy Use the formula dx Ay lim Ar¬0 Ax f(x + Ax) – f(x) lim Ax→0 %3D %3D Ax dy when y = dx 2 to find x…

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Q: Use the chain rule to find dy/dx for th following : y= (ax+b)^5

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Q: Find the general sebution of the oDE dy Sin(x+y)+ Cos (X+y) %3D dx

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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.