Answer ALL questions. SHOW ALL WORKING BRFORE PICKING THE OPTIONS QI: Evaluate I = [x* In xdx (A) - In x-+c (B) 25 In x- 5 5 +с (С) In x-+c (D) +C 5x d Q2: If ff(x)dx= h, then h+cosx+ [f(x)dx (A) sin x (B) cos x (C) 0 (D) –h. d Q3: Find the differential coefficient of y=(x² -1)sin 2x at x=0. (A) –1 (B) 1 (C) – 2 (D) 0 Q4:Find the volume of solid generated when y= /x+1_is completely rotated about the x -axis 157 - unit (B) 2 57 - unit (C) Зл - unit (D) 5 57 - unit³ 7 with x=0 & x=3. (A) 1 dx is: (A) In(1)+k (B) In k +x (С) In x+1, kx (D) none of the above Q5: 1= *(x+1), x+1 (dy if y = xen2x* . (A) 0 (B) 1 (C) 2 (D) 3 40 dx Q6: Evaluate lim dy Q7: The gradient of a curve at any point is given by = 2(x-1) such that the point (4,5) lies on dx the curve. Find the area (in unit² ), bounded by the curve & the x-axis. (A) 3 (B) 4(C) 5 (D) 6 2y(x+1) 2x- y² y(x+1) (B) (C) x-y x-y² (D) 2.x - y? 2y(x+1) dy Q8: Find if (x+1)y² =x². (A) dx y(x+1) Q9: Find the equation of tangent to the curve y=x' at x=2. (A) 12y+x-98=0 (B) 12y+x+98=0 (C) y=12x-16 (D) y =12x+16 Q10: Find the equation of normal to the curve y=x' at x=2. (A) y=12x-16 (B) 12y+x+98=0 (C) 12y+x-98=0 (D) y =12x+16

Q: If F(x)=sin(7-x5-13-x³ +5-x). Calculate dF(x) = dx

A:

Q: Evaluate f sin(5/z) -dr Select one: a. 금cos(5/z) + C b. 5 cos(5/a) + C – cos(5/x) + C C. d. cos(5/2)…

A:

Q: Given the functions Az) = cos(x) and g(z) = x - 5x- 6, determine the domain of the combined fx)…

A:

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h (x) = sin 2x

A: We have to determine whether the function hx=sin2x is in the span of the functions fx=sin2x and…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT ●コヅシッシ 2*@*!??!!??! ¿¡ !?! Wa - XXX O * Take Aeikx+ Be-ikx &♪…

A: To Show: Aeikx+ Be-ikx = C cos(kx)+ D sin (kx) Now, cos(kx) = (eikx+ e-ikx)/2 sin(kx) = (eikx-…

Q: State the set of zeros of f(x)=2sin(x)cos(x) using set builder notation.

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Q: Prove the identity. Work on one side only. cos(4x) = 18 sin² x+8 sin ¹ x

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Q: Algebraically explain that cos(x+1) function is DIFFERENTIABLE everywhere over its domain.…

A: f(x) = cos(x+1)

Q: 2 Evaluate: [5 cos(5)x – 5 csc² (x) ] dx COS

A:

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.