x-4y lim (x, y)-(0,0) 6y+7x 3 A O 7 .BO 0.c O does not exist. .D O H/7

Q: x sin(2x) 1- cos(x) limr→0 | А. О В. 1 С. 2 D. 4 E. the limit does not exist ||

A: The given expression is limx→0xsin2x1-cosx. Evaluate the limit limx→0xsin2x1-cosx as shown below.

Q: (2 cosh z, sinh z, 2 0. Then the lim f(x) A does not exist B is 2 C is 1 D is 0 B

A:

Q: Prove that

A:

Q: C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

A:

Q: ´e&z – z² I< 0 Evaluate the following limits for h(x) = %3D 1- 6z | (1) lim h(x) (ii) lim h(x) (iii)…

A: Given:  hx=e6x-x2,     x&lt;01-6x,       x≥0 To Find:  To evaluate the following limits:a limx→0-…

Q: Let y(t) denote the solution of the given initial value problem. Is it possible for the…

A:

Q: x2 + 0x – 4 lim x-2 x - 2 Enter I for oo, -l for -co, and DNE if the limit does not exist.

A:

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

A:

Q: The Michaelis-Menten equation for the velocity v of the enzymatic reaction at the concentration [S]…

A:

Q: Find lim (x,y)→(12,3) xy cos(x – 4y). OS 1. –36 2. 36 3. 3 4. 0

A:

Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

A:

Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

Q: 5x*e", 0S1 y(x) =

A: Given

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: 16x4+9y12 (x,y) (0,0) 4x²+3y6 Show that lim does not exist.

A:

Q: (t + At)2 – 7(t + At) + 3 – (t2 – 7t + 3) lim At0 At

A:

Q: lim (x,y)→(0,0) x²y 22 +y? Find the limit

A: In this question, we need to find the limit of multivariable function by using ε-δ definition.

Q: lim, „(Væ² + x – x)=? O a. 0 O b. 1 O c. Limit does not exist O d. 00 O e. 1/2

A: In these type of questions just rationalize the given term and simplify the fraction before finding…

Q: f(3+h) – f(3) lim h 0 ere f(x) = 7x² + 2. Enter I for oo, -I for -o, and DNE if the limit does not…

A: We will apply the limits

Q: b) If y(t) is the solution satisfying the initial condition y(0) 1, find the value of lim y(t).

A:

Q: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given:  The function y=x2+2x+1x, x≠0 To Find:  a The limit of y as x approaches positive infinity.b…

Q: Vx + 32 - 5 Limit. lim x--7 X + 7 O 0.1 O Does Not Exist (DNE or tco) O 10 O 1.4 O 5

A:

Q: 2. Given the function y = [(x-1)3 – 1]/(x), (x#0), find: (a) the limit of y as x approaches 0. (b)…

A:

Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

Q: valuate the limit 8x2 – 9x – 9 lim x→-o 7 – 7x – 10x2 E the limit does not exist enter DNE. imit =

A: We have to find limit

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Along the path x = e find lim (1,y)→(1,0) y2-6ry 3x-y-3 O 2 O does not exist O -3 O 3

A:

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: How can I find A, k, and C with the following information? L(t)=-(A/k)e^(-kt)+c Lim as t approaches…

A: Given function,

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

A:

Q: 8. Consider the solutions Y(t) of Y'(t) + ay(t) = de-bt with a, b, d constants and a, b > 0.…

A:

Q: 2. lim (x,y, Z)-) (0,0,0) EYaluate ベtyナスス

A: If limit depends upon the directions then limit does not exist.

Q: True or false? If k &gt; 0, then all solutions of y' = −k(y − b) approach the same limit as t →∞.

A:

Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

Q: (4x 5y) (z,y)→(1,1) 5x2- 7y lim O 1/2 O 1/2 O Limit DNE

A: We need to evaluate the following limit limx,y→1,14x-5y5x2-7y

Q: Find the limit. 1 t1 5 lim 4e 4 1t t 0 t t LC

A: First we take the limit inside and simplify

Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

A:

Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

A:

Q: 8 lim r→8 r2 8x Enter DNE if the limit does not exist. Limit =

A: Given limit:

Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: S (2t)*dt lim x→ =? х* — 1

A:

Q: If y = y(x) is a solution of y + 5y = 3e-2x + 3. Find lim y(x). x00 3 7 b) O Does not exist. 2 3 f)…

A:

Q: S(-1- x) + 1 if e+ - 2 Let f(x) = %3D 3x +7 if x = - 2 Calculate the following limits. Enter "DNE"…

A: We have to find the limit.

Q: {fn(x)} = {n²x(1 – x)"} for æ € R and n = 1, 2, 3.... | 1.find pointwise Limit

A: The given function is, fn(x)=n2x(1-x)n

Q: -5x? + 2x for æ 0 According to the definition of derivative, to compute f'(0), we need to compute…

A:

Q: 6zy lim zy)(0,0) z* + 3y

A: Suppose we are approching (0,0) along x-axis (y=0). Now we get lim(x,y)→(0,0)6xy3x4+3y4=limx→0…

Q: What is lim ZH00 2+1 4z2 A -2 в c) D) 1 E) The limit does not exist. 1/4

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.