lim< t², t→1 t²-1 t-1 . 1-t> = <3, 1,0> AO <1, 3,0> BO <1, 2,0> .CO <1, 0,3> .DO

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: lim (4x – 3y)= -11 Prove that (r.,v(-2,1)"

A:

Q: lim (Vx² +1 – (x+ 1))

A:

Q: Let z = e**y* , x = tan¬²(st5) and y = əz Evaluate as (2s+t)²* Select one: O a. 2xy³e{x³y?} t5 t –…

A: Given,

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: lim cos x+4e* is 5er

A:

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: 2 - Jx - 3 – v 4) lím エ→7 x² – 49

A: Given: ⇒limx→72-x-3x2-49

Q: 2. point Find the largest interval on which the Existence and Uniqueness theorem for hi order linear…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

A:

Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

A:

Q: 1 lim (x + 2)² cos x→-2 г2 — 4

A:

Q: Find lim [x +i(2x + y)] z→1-i iz3 – 1 lim z→i z+i

A: a) Given that, limz→1-ix+i2x+y It can be written as, limx+iy→1-ix+i2x+y

Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

A:

Q: 2 -t+ sin t 11. lim t-00 t+ cos

A: We have to solve: limt→∞2-t+sin tt+cos t

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

A:

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

A:

Q: 1-sin x x1 + cos2x 2 5) lim 6) lim sin x-cos x TC 4

A:

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: lim b→∞ 2x 22 x² + 1 -b dx.

A: To solve the following problem of integral and then find the limit

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: Compute lim 240 sinx² +1-cos.T 2 I + (1+x²) ²/2²)

A:

Q: 7t + 4 lim t→-∞ t2 + 1 – 7t

A:

Q: 4) Graph y = arcsin x and z = arcsin (x-2) and w= arcsin (x/2) on the same axes Remember that these…

A:

Q: #1. lim t-tvt 213/2 12 +3t – 5 t→ 00 #2. lim x → - o0 x' +1 #3. lim tan1 (In x) x → 0+

A:

Q: The value of a and b so that X(1 + a cos x)- b sin x lim =1 are .3 to 3 3 5 (b) 2 2 (a) 3 5 (c) 2 2…

A:

Q: 26.lim(1 + cosx)2secx x 2 27.lim (G– x) tgx 27.lim ( - 2

A:

Q: olve 1 1+xsin limy-0 1+xcos-

A: To find limx→ 01+xsin1x1+xcos1x

Q: Show all work! Find the maximum, minimum, and saddle point of f(x,y) = cos(x)+ (1/y^2 + 1/x)+1

A: We will use the basic knowledge of 2-variable calculus to answer this question.

Q: Evaluate: / [sec (x) – ese²(x) ]dv А tan (x) - сo(х) +с ® ;o*(x) + w«*(+) + Cc (B sec (x) – csc (x)…

A: We have to solve this integration

Q: lim t→0 4t² + 3t sin t +2

A: To evaluate the following limit.

Q: If x(t) , X(f), then show that x(t) cos (@- w. 2 (@ + w.).

A: To find fourier transfer of given system first expand cos wt in form of Eulers form then use the…

Q: Find -3) 2/2 lim xxx+1,

A:

Q: Of of Let f(x, y) = x°y² tan y Then x +y. equals

A: The derivative of a function of two or more variables with respect to one variable, while the others…