(a) In(1– x) +xe? (b) 2х 2x 1-cos(x) (d) V1+x-1 Check and briefly explain how to avoid the loss of significant figures in the calculation of the following formula in close proximity.

Q: T/4 (x² − 2x + sin x + cos2x) dx. - Compute π/4 Hint: Try to save as much time as possible by using…

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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…

Q: (a)     ? = sin−1       (b)     ? = cos−1       (c)     ? = tan−1

A: asinθ=1215θ=sin-1(1215)θ=53.13ob)cosθ=915θ=cos-1(915)θ=53.13o

Q: In [tan (5 + )| +o sec x dx 4 2

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Q: One of the values of x from the equation 2 csc(x) = 4 over the interval [0, 2π) is 5.

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Q: 13x Find the derivative of the function y = 2 tan¬1 (5x ). (Use symbolic notation and fractions…

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Q: To show that rπ/2 sin" x cos" x dx: (m - 1) (m- 3) ... × (n – 1) (n - 3)... (m + n) (m + n - 2) (m +…

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Q: C: Proof that ( a) L (cos²t - sin²t) S s² + 36

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Q: Given that 7g(x) – 3x sin(g(x)) = 5x? + 7x – 24 and g() = 0, find g (). I(}) =

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Q: (c)(i) Use the substitution x = tan²0 to show that √x 。 (1 + x² ) ² (ii) Hence find in simplest…

A: We have to show                            ∫01x1+x22dx=∫0π42sin2θdθ     by substituting  x=tan2θ and…

Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: (а) Vr3 3 – 1 (b) 2, х3 cos2xdx

A: Integration is the process of finding the anti-derivative of the function. The integration is done…

Q: It can be shown by induction that the nth derivative of the sine function is given by the formula d"…

A: Givendndxn(sin x)=-1n-12cos xn odd(-1)n2sin xn evenTo findwhether the given formula is correctTo…

Q: Use the formula £{t^f(t)} (s) = (-1)^(((s)) to help determine the following the expressions. (a) L(t…

A: Solution:-

Q: (9) If sin(A) = /2, sin(B) = - ½, "/½ < A < r, and n < B < 3*/2, find cos(A + B) (A) 0 (B) /2 (С) —…

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Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³; (4) y = x sinh 2x-cosh 2x (2) y =…

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Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: In(arctan(x)) da 1+ x² 1

A: Given that a integration and we solve this integration by using general formula of integration.…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT yyy Ü♥¯ ¶ ☆ @ ! ! ?? !! ? ?! ¿ ¡ !? S❀ W X Х Х Х Х A * ✓✓✓ DO -…

A: We have not any digital tool .

Q: d 6. dx sine 1 sin(x²) (B) (D) – sint=") (A) – x sin(x²) (C) x sin(x²)

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Q: If Log (x +1)-lo83(x-1) 3. 36-x arc sin! The inverse of (3メー2)

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Q: Consider the following three functions: f(t) = sin((t-2)), g(t) = ㅠ sin ·(t — 4)), 31 ) =…

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Q: dx Evaluate: /9 – x² A @ sin -1 +C .3. 1 3 sin +C 3. B

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Q: Q11] Using the properties of the FT, calculate the FT of the following functions: (a) x¡(1) = 5 +3…

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Q: What is the second derivative of In(x4– 1)? - 16x9+ 12x6– 12x² (A) (x4– 1) 2 4x3 In (B) - 4x6– 12x2…

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Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral