waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan” (x) + C m (m + 1)(x) + n (m-1)(x) + C tan m-1 1 tan n(m +¹)(x) − __ ___ tan (m − ¹)(x) + C m-1 −tan (m +¹)(x) + C tan

Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

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Q: 10. Given: f(x) 3= d) tan(A – B) and g(x)=x² +8 x- 5 Find: a) (f-g)(x) (g •(8))(x) i) (g-f)(3) b)…

A: Given that f(x)=1x-5 and g(x)=x2+8   (a) f-gx f-gx=fx-gx               =1x-5-x2+8…

Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

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Q: x2 1+x2 x3 3 + C x+ x3 3 Ox- In (1 + x²) + C Ox – tan-1 (x) + C X - O In (1 + x²) + C

A: We have to find the indefinite integral

Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: 23. Integrate: S x+2 dx 2 A. V1– x² + Sin-1x + C C. -V1– x² +Sin-1x + C B.V1 – x2 +Sin-1x + C D. –V1…

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Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) +…

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Q: 2 1.f(3x²+5) cos 2xdx 0

A: We need to perform integral. NOTE - As per Bartleby guidelines we can solve one question from…

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

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Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: dx - = In[F(x)]+C•What is F(3) if C= 0? For (1+*;_u®L x)(g*+ x)

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Q: Evaluate tan" (x) sec²x dx m 1 1 n (m + 2)(x) + tan -tan" (x) + C m+2 m 1 -tan (m + 1)(x) — . m+1…

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Q: 4. * S sec? (4t) (3 – tan(4t))³dt A C 1 (3 - 4 tan (4t))* + C (3 – tan (4t))ª + C 16 - - - - | - В 1…

A: The objective is to find the integration.

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: . What is F(/3) if C = 0?

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Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: -tan (m + 1)(x) + C tan I + m um + ( x ) (x + ₁)² I m+3 1 с

A: Using substitution then integrating we get correct answer as (C)

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

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Q: dr (g) sin(2x) + 4 sin r

A: Sorry we can answer first question as per honor policy. Please resubmit other question as well to…

Q: m-1 1 + m 1 m m+2 ¹tan (+2)(x) + —tan" (x) + C m-1 1 + m 1 m+3 Ɔ+ (*) (1 - 1)² + (x) (1 + m) U²1-…

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Q: 1 Find that antiderivative of the function whose value at X = –1 is x2 + 4x + 5 0. x + 1 In |x+5 -…

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