Find the limit, if it exists. Be sure you can explain your answer. lim (9r (1,4) >(0,0) - 8y? + 6e²² v°, cos(8ry)) Use "infinity" for "00" and "-infinity" for "-o0". Use "DNE" for "Does not exist".

Q: (e" -e¹"), then write: e¹ and e¹*. 1 If cos(x)= os(x) = -(e* + e^ª) and sin(x) = -— (e“ - e²"), e™“)…

A: We have to find the values of

Q: Simplify and Solve lim i sincuat) +5 sin (4t+) -T and lim i sincuat) +5 sin (4t+) -T

A: We will use property of definite integral  ∫-aaf(x)dx=∫0af(x)+f(x-)dx

Q: cos² 0 - 1 1 inet 12. lim

A:

Q: Seco-Cose Lim Cos h h2 h -2

A:

Q: Graph the function: Y=sin-(2x) – 2

A: Graph the function:     Y=sin-12x-π2

Q: sin?x-1 10. lim sinx-1 2

A: Let f,g be functions which are continuous and differentiable. If while computing the limit…

Q: (d) lim 140 sin(2x) – sin(3x)

A:

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: Solve the following linear programming problem. Restrict x 2 0 and y 2 0. Maximize f = 6x + 8y…

A: Step:-1 Given that  Maximize f = 6x + 8y subject tox+y≤82x+y≤14y≤4x, y≥0 First we solve all…

Q: Q2/plot the radiation pattern u (0, p)= Sine cosp in coordinate XY, XZ With illustration on the…

A: To plot the radiation pattern u(0, 0) = Sine cosp, we need to first understand the equation and its…

Q: sinx lim x→0 3x

A:

Q: Q3. Evaluate ". -2n sin²0 de 5+4cos0

A: To Determine :-  ∫02π sin2 θ5 + 4 cos θ dθ

Q: с. Graph and find the domain and range for y=sin'(x) – 3

A: Given function is  y = sin^2(x) - 3

Q: S.S. X x Arcsin y 4 yª dydx

A: Reverse order

Q: lim X4+0 X+1 5 +4 xf txb

A:

Q: sin(x²) 1+0- e2r – 2x – 1° Evaluate lim

A: This question is related to limits, we will solve it using given information.

Q: . Graph the function y = - 2 cos(2x - π).

A: given,         y=-2cos2x-π

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

Q: S dz zlnz (Inz)²-1 Select one: O A. Q B. O C. Q D. arcsec(Inx) + C arcsin(lnx) + C arccot(Inx) + C…

A:

Q: Simplify: 3 (4x³y'z*)(16x'y^z*") (4x's ,5, 4 (1}° 18x'y¯z

A:

Q: Use the product rule to find the derivative. Simplify the result. d :[V¤(13x +2)] dx

A:

Q: Evaluate: 0 tan-¹ (0) de Ô arctan(9)–0 2 arctang+ -arctan0+C 0—arctan(0) +C

A:

Q: (Extra). Graph. Y=3-Sin (x/2 + pie/6)

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: