x2 – 3x Performing the integral /- -dr yields: (x²+ 1) (x– 1) 2 a. tan –'(x) – 2x + 3 + c O b.2(x²+ 1) In(x-1) + c Oc 2 an - (x) – m(x?+1) + -n(x– 1) + 3 Lim(x²+ 1) -In(x–1) - + c x- 1 4 O d. In(x²+ 1) + 2ln(x- 1)+ e

Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

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A: To find the limit  lim(x,y)→(0,0)(x2+y2)log(x2+y2)

Q: Q4. (a) Evaluate the definite integrals: (i) ſ(2 – 5/1 – x² }tx_ (ii) [sin 2x cos 2x dx (iv) [":…

A:

Q: (а) 1716 — 8г' + 3х — 4 + 1/3 + Vт — V:3 (b) sin 5a - сos(х /8) + sec?(z/3) csc (5x) сot (5x) (с) 2…

A:

Q: "(2) – 16f(2)) sinh(4x) dr Find the value of in terms of f(0) if f(a) = f'(a) = 0. %3D f(0) O f(0)…

A: See the calculation below  Fourth option is correct

Q: Apply the special case of the general power rule d/dx [h(x)]2 = 2h(x)h(x) and the identity fg =…

A: dhx2dx=2hx·h'x  &  fg=14f+g2-f-g2

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

Q: If f(2010) = π/2, f(2x) = f(x)Vx E R and f(x) is continuous for x E R, then the value of…

A: Let us solve above problem by using L'Hopital rule

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A: Given function is  fx=4x2+16x+25 To find f'(x) using f'x=limh→0fx+h−fxh

Q: b) lim (4-5 ln(x) +8e¹00-2) 14X

A:

Q: f(x) = x+1 g(x) = log(102tan¹(x)), h(x) = x . 1) Find lim f([h(x)]²) X-1 2) For the following…

A: Step 1:Step 2: Step 3: Step 4:

Q: 5. Find limx→∞ f (X), if it exists. (a) f(x) = log(x² + 2y² + 4z²) x² + y² +2² (c) f(x) = e(x+y)²…

A:

Q: Calculate the difference quotient for f(x) = 5 – x² at a = 4. (Express numbers in exact form. Use…

A:

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

A:

Q: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

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A:

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A:

Q: lim (sgn(x² – 1) + [x + 3]) = ? X→-- 2

A: see below the answer

Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

A:

Q: f" (h+x)-j" (x) li h→0

A:

Q: ) (a) Let f(x) = 6 + f'(x) and f'(4). f'(x) = ƒ'(4) = - x + C 6 Find

A: As per the guidelines  we are supposed to answer only one question at a time. If you want answers of…

Q: the integral of (15tan-1(x))/x2

A:

Q: 10. y"of y = arc tan

A:

Q: f(x) = 2x* + 2x? - 5x sin2 (x)- 5 g(x) = 2x* - 8x- 3+5x cos2(x) Two functions are defined as…

A:

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

A:

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)