Graph and discuss the continuity of the function sin xy f(x, y) = if xy + 0 ху 1 if ху — 0

Q: Suppose f"(x) = - (sin(x)), ƒ'(0) = –2, and f(0) = -3. %3D Find f(1/4).

A: Given,          Suppose f''x=-sinx , f'0=-2 and f0=-3.

Q: Determine the intervals of continuity for the function: f(x) = over the interval of 0 < x < 2n…

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Q: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: Use the Second Fundamental Theorem of Calculus to find F'(x).

A: The function is given as

Q: Let F (16xyz + 7 sin x, 8x² z, 8x²y). Find a function f so that F f(0,0, 0) = 0.

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Q: az əz Use implicit differentiation to find and, . əx əy' xy'z³ + x'y°z = x + y + z

A: Given. xy²z³ + x³y²z = x+ y +z We need to use  implicit differentiation in partial derivative and…

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Determine if the function is continuous at point (0,0): F(x, y)=**y°cos(x*+y³) (x²+y²)2

A: Given that Now take x=0, Now take y=0,

Q: Find the absolute maximum of the function f(x)=sin(2x)+cos(2x) on the interval [0, pi/6].

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: State the domain on which the function is continuous. h(x) =(cos(1/x))/(x2−1)

A: Domain is defined as the set of all points over which a function is defined.

Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: y=x-2cosx Differentiate the function. dydx=ddx(x-2cosx)=1+2sinx

Q: 43. Graph and discuss the continuity of the function sin xy if xy + 0 f(x, y) = ху 1 if xy = 0

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

A: When the limit exist or equal to 0 then the series is convergent otherwise divergent.

Q: Write the interval of continuity for the function below: cos(x)/25 – x² - f(x) = x2 + 11x + 28

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Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

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Q: use the Laws of Continuity and Theorems 2 and 3 to show that the function is continuous f (x) = ex…

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Q: The derivative of f(x) = tan- is: Select one: O a. O b. O C. O d. 1 x² cos² 1 -1 x² cos² 1 xcos² 1 F…

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Q: Determine if the function is continuous at point (0,0): F (x, y) _x³y°cos(x³+y³) (x²+y²)²

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Q: Show that the function is continuous. f(x) = cos(x 2)

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Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: Let f be given by if x COS x Show that f is continuous everywhere.

A: Given: f(x)=sinx , if x&lt;π4cosx, if x≥π4

Q: 4. Find and sketch the domain. f(x, y) = sin='(y - x)

A: fx,y=sin-1y-x

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 5 F(x) cos (t*)dt. CoS…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Let f(x)={tan(2x) ax+b if x>0 if x<0 For which values of a and b is f(x) differentiable for every…

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Q: Let f(x) ∈ R[x]. Suppose that f(a) =0 but f'(a) ≠ 0, where f'(x) isthe derivative of f(x). Show that…

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Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: Let fn f, where if 0<<! Sn(x) ={ S 2-a if 0<x<1 and f(x) if a = 0 Then lim sup fn (x) – ƒ (x)| =

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Q: Find f. f"(x) = cos(x), f(0) = 1, f'(0) = 8, f"(0) = 6 f(x) = sin x + 7x/2 + 7x +8|

A: We will first find the general solution of f"'(x)=cos(x)

Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

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Q: If the relation x z² - 5xy z-x2-y 0 defines z as a differentiable function of x and y. By using the…

A: Solution

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: The function f(x) sin x + cos x is an even function. True False

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. '6 G(x) :…

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Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: Determine if g is differentiable at a = 0 if 2 cos-1 if – 1 0. x + cos x

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Q: For the set of functions {sin(x), sin(2x), sin(3x), ...} = {sin(nx)}, n = 1,2,3, ... on the interval…

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Q: Limit as t goes to 0 of    (t^3+3t) / sin (5t)

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Q: Find the value of c that makes the function continuous at x = 0.

A: Given function:

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

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