4x e lim x→0 r2

Q: x²–1 For S dx,x

A: Given,             ∫x2-1xdx

Q: 6. lim t+0o e3t + 4t

A: Given: limt→∞t2e3t+4t To determine: The value of the given limit.

Q: lim, s0¤(t) = 1? Оа. "+а — 0, z(1) — 2. 0, г(1) — 2. ОБ. — - 0, 2 (2) — 1. Ос. - 2г — — 0. 0, æ(1)…

A: To determine which of the following initial value problems has a solution xt.limt→∞xt=1a x'+x=0,…

Q: Solve the following nonhomogeneous ODES. (a) y" = -4y+ e2";

A:

Q: Which of the following is not true? 5 dx dx ® (Α Sº o 25-x² lim c+5-0 25-x² ® √ in(x²) dx = lim_…

A: We have determine the integration

Q: Find lim e" dt O 1/e 1

A: This is a special integral function, apply linearity and then solve.

Q: Find dy dx 2 for x²exy = 5 WA/

A:

Q: Which of the following is not true? A Sin(x²)dx= limin(x²)dx c (B) None of the given choices .5 dx ©…

A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

Q: Which of the following is not true? ,5 Ⓒ √√² 25²x x² = 11m -√² 25-4x2² dx dx A lim o c+5-0 3 3 dx dx…

A: We have to find out the option

Q: 1 lim E n→ 00 i=1 'n² + i?

A:

Q: dx 1. Evaluate e x(In x)3

A: We’ll answer the first question that is question (1) since the exact one wasn’t specified. Please…

Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

A:

Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: 1- yln ydx + (1+ x² )dy = 0

A: ** As per our guidelines we are allowed to answer only one question a time. Kindly please re-post…

Q: -2x 39. lim (e* cos x)

A:

Q: 21 (e) If(x)| dx (f) f(x) dx 16

A:

Q: e2 1 dx x In x e

A:

Q: XA - ХА + yl th

A:

Q: lim In(12x+ 1) csc(4x) A) 0. B) 1. C) е. D) 3. E) 0.

A:

Q: 1. Find x'e *dx if it exists.

A:

Q: 4. lim (3x e*) = %3D 5. lim (3x e*) %3D D

A: Our Aim is to evaluate the following limits given below:-(a)limx→-∞ 3ex x(b)limx→∞ 3ex x

Q: 3. Derive the reductive formula for f sec" (x) dx.

A:

Q: Q2: Fill the blank: 1) lim (1+)5x x48 4x 2) lim x.e-3x = X-8 3) (csch-¹x³) = = 4) ₂° e-*dx 5) S-…

A:

Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent

A: we have to identify the given sequence is convergent or divergent

Q: m/LIM K 85° 65° L J M 150°

A: Answer

Q: e" sin x = x- xy S1

A:

Q: lim equals O a. None Ob. -1 Oc i O C. Od. O d. -i | O e. 1

A:

Q: N= 8%° + 3s $1

A:

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given,

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

A:

Q: (2+k)dr Evaluate 1– sec (x+a) 1- sec

A: ∫2+k1-secx+adxTake the constant out=2+k·∫11-secx+adx Now,    ∫11-secx+adxLet…

Q: 1 x" cos (nx)dx 1+n? Evaluate lim

A:

Q: Which of the following is not true? C 4dx 4dx A So √X(X+6) = lim So c+∞ ¹0 √x(x+6) 5 dx dx B S = lim…

A:

Q: 3. X-メ Find d x at x=\

A:

Q: In3 x B. Evaluate ( [e2x+3y dy dx

A: We have to integrate

Q: Which of the following is not true? A √ in(x²) dx = lim_ sin(x²) dx 3 3 dx dx Ⓒ 1² B In(x²) - = lim…

A: Solution is done in step 2

Q: lim e 0 t/ Select one True False

A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

Q: c B None of the given choices 3 3 dx dx © √₁³ (x²) = lim + √c in (x²) 1 4dx 4dx Ⓒ √ √X(X + 6) D =…

A: These are the problem of improper integral and convergence/divergence of improper integrals.

Q: x'sec'ydy – (1 – 2x²tany)dx = 0

A:

Q: 1+ 2x dx. Compute x2

A: Now we have to compute   =∫1+2xx2dx=∫1x2+2xx2dx=∫1x2dx + ∫2xdx=∫x-2dx + 2∫1xdx                ......…

Q: 2 x²e¬2® dx. Compute

A:

Q: 3 Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

A: This is a problem related to triple integration. Based on the general formula and concept we will…

Q: Find d if y = In(x³/x + 9). dx

A: Known fact: ddxfgx=f'gx g'xddxfg=fg'+gf'

Q: Find y''of 4cos(x/2)+e^-2x

A:

Q: Q.1 Determine a, b, c, d & e such that cos ax + bx+ cx + dx + e 2 lim-

A: To find the values of a,b,c,d and e

Q: Solve ODE (1 + x²)dy + (xy + x³ + x)dx <=0

A: